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in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we have 36 minus 120 . it 's going to be negative 84 all of that 6 . so you might say , gee , this is crazy .
or is x = -1 +- ( sqrt -84 ) /6 more simplified ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
now , this is just a 2 right here , right ? these cancel out , 6 divided by 3 is 2 , so we get 2 . and now notice , if this is plus and we use this minus sign , the plus will become negative and the negative will become positive .
at 14 , can i write x = 2+- ( sqrt 39 ) /3 as x = 2+- ( sqrt 13/3 ) ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
is there a way to write the quadratic formula w/o filling nearly half a page ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so this actually does have solutions , but they involve imaginary numbers . so this actually has no real solutions , we 're taking the square root of a negative number . so the b squared with the b squared minus 4ac , if this term right here is negative , then you 're not going to have any real solutions .
what is the meaning of no real root ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so that 's the equation and we 're going to see where it intersects the x-axis . where does it equal 0 ? so let me graph it .
what would happen if the original equation was not equal to 0 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's what the plus or minus means , it could be this or that or both of them , really . now in this situation , this negative 3 will turn into 2 minus the square root of 39 over 3 , right ? i 'm just taking this negative out .
at 1why ca n't sqrt of 39/3 be simplified to sqrt of 13 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
and let 's do a couple of those , let 's do some hard-to-factor problems right now . so let 's scroll down to get some fresh real estate . let 's rewrite the formula again , just in case we have n't had it memorized yet .
how is relevant to anything in the real world ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ?
what if b was negative ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ?
would you plug it in as positive or negative for when the formula calls for -b ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
in the future , we 're going to introduce something called an imaginary number , which is a square root of a negative number , and then we can actually express this in terms of those numbers . so this actually does have solutions , but they involve imaginary numbers . so this actually has no real solutions , we 're tak...
can someone else who has already learned imaginary numbers help me figure out what the solution ( s ) to the equation introduced around is ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
will you say the quadratic formula is important ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things .
is there a major difference between the formulas , if one at all ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
its vertex is sitting here above the x-axis and it 's upward-opening . it never intersects the x-axis . so at no point will this expression , will this function , equal 0 .
for quadratics that do n't reach the x-axis is there a way to find the ( x , y ) where the curve is at a minimum/maximum ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we could say this is equal to negative 6 over negative 3 plus or minus the square root of 39 over negative 3 . now , this is just a 2 right here , right ? these cancel out , 6 divided by 3 is 2 , so we get 2 .
my question is algebraic : how are the x 's on the right side isolated/removed ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's what the plus or minus means , it could be this or that or both of them , really . now in this situation , this negative 3 will turn into 2 minus the square root of 39 over 3 , right ? i 'm just taking this negative out .
ca n't 39 be factored into 3 and 13 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
is there a reason that the quadratic formula is similar to the formula for the axis of symmetry of a parabolic equation ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
this is a quadratic equation where a , b and c are -- well , a is the coefficient on the x squared term or the second degree term , b is the coefficient on the x term and then c , is , you could imagine , the coefficient on the x to the zero term , or it 's the constant term . now , given that you have a general quadra...
does the equation have to be equal to zero in order for the quadratic formula to work ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we could just divide both of these terms by 2 right now . so this is equal to negative 4 divided by 2 is negative 2 plus or minus 10 divided by 2 is 5 . so that tells us that x could be equal to negative 2 plus 5 , which is 3 , or x could be equal to negative 2 minus 5 , which is negative 7 .
i 'm confused with an exercise in the module ... why does 2+or-2sqrt21/-10 simplify to 1+or-sqrt21/-5 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so you get x plus 7 is equal to 0 , or x minus 3 is equal to 0 . x could be equal to negative 7 or x could be equal to 3 . so it definitely gives us the same answer as factoring , so you might say , hey why bother with this crazy mess ?
near could n't sal have just devided the thing by six ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 .
i do n't understand once you started square rooting 156. what happens ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ?
when b is a negative , do you square it as a negative , ( -b ) ^2 or take the opposite of the square - ( b^2 ) ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so 156 is the same thing as 2 times 78 . 78 is the same thing as 2 times what ? that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root o...
how would you solve d^2-8d=0 by completeing the square and 4x^2-7=0 using the quadratic formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ?
7 if b was a negative to start out with would that make it a positive when you put it into the formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 84 . we make this into a 10 , this will become an 11 , this is a 4 . it is 84 , so this is going to be equal to negative 6 plus or minus the square root of -- but not positive 84 , that 's if it 's 120 minus 36 .
so i divide by 11 to make x^2+ ( 4/11 ) x-13/11=0 , so the sum or s is the negative of the middle term or s=-4/11 and the product or p=-13/11 what two identical numbers add to -4/11 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we could say this is equal to negative 6 over negative 3 plus or minus the square root of 39 over negative 3 . now , this is just a 2 right here , right ? these cancel out , 6 divided by 3 is 2 , so we get 2 . and now notice , if this is plus and we use this minus sign , the plus will become negative and the negative w...
ans : -2/11 what is -2/11 squared ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
b squared is 16 , right ? 4 squared is 16 , minus 4 times a , which is 1 , times c , which is negative 21 . so we can put a 21 out there and that negative sign will cancel out just like that with that -- since this is the first time we 're doing it , let me not skip too many steps .
ans : 4/121 but i need -13/11 or -143/121 so what do i subtract from 4/121 to get -143/121 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
can you use the quadratic formula under every circumstance with 2nd degree polynomials ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so this will be equal to negative 6 plus or minus the square root of 39 over negative 3 . or we could separate these two terms out . we could say this is equal to negative 6 over negative 3 plus or minus the square root of 39 over negative 3 .
is there some sort of rule to follow when moving the terms that i do n't know about ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so that tells us that x could be equal to negative 2 plus 5 , which is 3 , or x could be equal to negative 2 minus 5 , which is negative 7 . so the quadratic formula seems to have given us an answer for this . you can verify just by substituting back in that these do work , or you could even just try to factor this rig...
is the answer obtained using `` completing the square , '' when factoring a quadratic equation , the same as when using the quadratic formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so i have 144 plus 12 , so that is 156 , right ? 144 plus 12 , all of that over negative 6 . now , i suspect we can simplify this 156 .
can anyone tell me at the end there , where it was -12 +- 2* sqrt ( 39 ) and all of that over -6 why did n't sal just divide the -12 and -6 by -6 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
is the quadratic formula useful ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ? 4 squared is 16 , minus 4 times a , which is 1 , times c , which is negative 21 .
if b is already negative , when you go to plug in your numbers into the equation , would you change b to a positive ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
let 's rewrite the formula again , just in case we have n't had it memorized yet . x is going to be equal to negative b plus or minus the square root of b squared minus 4ac , all of that over 2a . i 'll supply this to another problem .
instead factor , can you use : x=-b+or- square root b^2-4ac/2a ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
you say what two numbers when you take their product , you get negative 21 and when you take their sum you get positive 4 ? so you 'd get x plus 7 times x minus 3 is equal to negative 21 . notice 7 times negative 3 is negative 21 , 7 minus 3 is positive 4 .
is x is left side and non-x ( not a x ) is in right side ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that is a , this is b and this right here is c. so the quadratic formula tells us the solutions to this equation . the roots of this quadratic function , i guess we could call it . x is going to be equal to negative b. b is 6 , so negative 6 plus or minus the square root of b squared .
is the graph of a quadratic function a parabola or a straight line ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
let 's see where it intersects the x-axis . it goes up there and then back down again . so 2 plus or minus the square , you see -- the square root of 39 is going to be a little bit more than 6 , right ?
so someone shared that they had learned it this way which was to the nursery rhyme `` pop goes the weasel ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
can there be a `` d '' variable in the quadratic formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 .
how would you factor a square root ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ? 4 squared is 16 , minus 4 times a , which is 1 , times c , which is negative 21 . so we can put a 21 out there and that negative sign will cancel out just like that w...
im confused as to why you made the 16 - 4 a 16+4 in the first example , why do the negatives cancel out ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
what does the b in the quadratic formula stand for ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
how do you know when to use the quadratic formula or completeing the square or square roots ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so let 's speak in very general terms and i 'll show you some examples . so let 's say i have an equation of the form ax squared plus bx plus c is equal to 0 . you should recognize this .
how would you use completing the square on ax^2 + bx + c = 0 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
what type of equations should we use the quadratic formula with ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that is a , this is b and this right here is c. so the quadratic formula tells us the solutions to this equation . the roots of this quadratic function , i guess we could call it . x is going to be equal to negative b. b is 6 , so negative 6 plus or minus the square root of b squared .
how do you figure out what the quadratic function will be equal to ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
what is this going to simplify to ? 36 minus 120 is what ? that 's 84 .
why does sal subtract 36 from 120 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
is there any easy way to memorize the quadratic formula , such as an acronym or mnemonic ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
a little bit more than 6 divided by 2 is a little bit more than 2 . so you 're going to get one value that 's a little bit more than 4 and then another value that should be a little bit less than 1 . and that looks like the case , you have 1 , 2 , 3 , 4 .
how do you know which value belongs to each variable ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
it 's worthless . it just gives me a square root of a negative number . it 's not giving me an answer .
why ca n't you take the square root of a negative number without having to delve into the world of imaginary numbers ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
is the quadratic formula same for all equations ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 .
if you want to make the negative square root into an answer you use like -6plus or minus i times the square root of 84 divided by 6 right ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
b squared is 16 , right ? 4 squared is 16 , minus 4 times a , which is 1 , times c , which is negative 21 . so we can put a 21 out there and that negative sign will cancel out just like that with that -- since this is the first time we 're doing it , let me not skip too many steps .
why does the formula always have to be multiplied by 4 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so let 's speak in very general terms and i 'll show you some examples . so let 's say i have an equation of the form ax squared plus bx plus c is equal to 0 . you should recognize this .
why , if the roots of the equation , a ( x squared ) + bx + c = 0 , are d or e , de = c /a and d + e = -b /a ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
you would get x plus -- sorry it 's not negative -- 21 is equal to 0 . there should be a 0 there . so you get x plus 7 is equal to 0 , or x minus 3 is equal to 0 . x could be equal to negative 7 or x could be equal to 3 .
does anyone know how to solve x^2 - 63x + k = 0 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
it 's worthless . it just gives me a square root of a negative number . it 's not giving me an answer .
i took the test for the quadratic formula and i do not understand when a number has a square root or when you need to factor the prime factors out of that number ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
who made the quadratic formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so you 're going to get one value that 's a little bit more than 4 and then another value that should be a little bit less than 1 . and that looks like the case , you have 1 , 2 , 3 , 4 . you have a value that 's pretty close to 4 , and then you have another value that is a little bit -- it looks close to 0 but maybe a...
why ca n't i simplify -4 in the numerator and 2 in the denominator ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so this will be equal to negative 6 plus or minus the square root of 39 over negative 3 . or we could separate these two terms out . we could say this is equal to negative 6 over negative 3 plus or minus the square root of 39 over negative 3 .
how can a variable have two values ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 .
why does it have a square root ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 . 2 square roots of 39 , i...
ca n't the b^2 inside the square root be simplified ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's a nice perfect square . all of that over 2 , and so this is going to be equal to negative 4 plus or minus 10 over 2 . we could just divide both of these terms by 2 right now . so this is equal to negative 4 divided by 2 is negative 2 plus or minus 10 divided by 2 is 5 .
why do you divide by 2 on the last example ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
in the nursing field will i have to use the quadratic formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
what is the origin of the delta for quadratic formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
b is 6 , so we get 6 squared minus 4 times a , which is 3 times c , which is 10 . let 's stretch out the radical little bit , all of that over 2 times a , 2 times 3 . so we get x is equal to negative 6 plus or minus the square root of 36 minus -- this is interesting -- minus 4 times 3 times 10 .
why put the b^2 in the radical ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
and we had 16 plus , let 's see this is 6 , 4 times 1 is 4 times 21 is 84 . 16 plus 84 is 100 . that 's nice .
why did sal change 100 to 10 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so let 's speak in very general terms and i 'll show you some examples . so let 's say i have an equation of the form ax squared plus bx plus c is equal to 0 . you should recognize this .
is the vertex form of a quadratic related at all to slope-intercept form of a line ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
you would get x plus -- sorry it 's not negative -- 21 is equal to 0 . there should be a 0 there . so you get x plus 7 is equal to 0 , or x minus 3 is equal to 0 . x could be equal to negative 7 or x could be equal to 3 .
what is the two solution of x^2+10x+9+0 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
is it okay to use the quadratic formula if the variable is y but the formation of the equation is still in ax^2 + bx+ c = 0 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
how was the quadratic formula formed ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
there should be a 0 there . so you get x plus 7 is equal to 0 , or x minus 3 is equal to 0 . x could be equal to negative 7 or x could be equal to 3 .
x^2+4x=0 ) would the c equal zero or one ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
well , the first thing we want to do is get it in the form where all of our terms or on the left-hand side , so let 's add 10 to both sides of this equation . we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula .
3x^2+6x=-10 was equal to x=-1+-14i if you use imaginary numbers correct ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
notice 7 times negative 3 is negative 21 , 7 minus 3 is positive 4 . you would get x plus -- sorry it 's not negative -- 21 is equal to 0 . there should be a 0 there .
how would you get the x ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
but with that said , let me show you what i 'm talking about : it 's the quadratic formula . and as you might guess , it is to solve for the roots , or the zeroes of quadratic equations . so let 's speak in very general terms and i 'll show you some examples .
what are common mistakes that people make when solving quadratic equations ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
notice , this thing just comes down and then goes back up . its vertex is sitting here above the x-axis and it 's upward-opening . it never intersects the x-axis .
can it solve for a vertex without using the vertex equation ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
is it possible to use the quadratic formula if all of the values are positive ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
this is a quadratic equation where a , b and c are -- well , a is the coefficient on the x squared term or the second degree term , b is the coefficient on the x term and then c , is , you could imagine , the coefficient on the x to the zero term , or it 's the constant term . now , given that you have a general quadra...
how to illustrate the quadratic equation ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
78 is the same thing as 2 times what ? that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times...
where did the 2 go when dividing the numerator and the denominator of 12+- 2 square root 39 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so you 're going to get one value that 's a little bit more than 4 and then another value that should be a little bit less than 1 . and that looks like the case , you have 1 , 2 , 3 , 4 . you have a value that 's pretty close to 4 , and then you have another value that is a little bit -- it looks close to 0 but maybe a...
here 's how i got there : ( -3x^2 +12x +1 ) /-3 = 0/-3 x^2 -4x -1/3 = 0 x^2 -4x +4 = 1/3 +4 ( x-2 ) ^2 = 13/3 x = 2 +/- sqrt ( 13/3 ) where did i go wrong ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we could say this is equal to negative 6 over negative 3 plus or minus the square root of 39 over negative 3 . now , this is just a 2 right here , right ? these cancel out , 6 divided by 3 is 2 , so we get 2 .
we could just work out what [ b^2 -4*a*c ] is equal to and plug that into the equation , instead of needing to write such a complex formula , right ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
x is going to be equal to negative b plus or minus the square root of b squared minus 4ac , all of that over 2a . i 'll supply this to another problem . let 's say we have the equation 3x squared plus 6x is equal to negative 10 .
what was the complex solution to that problem ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
or we could separate these two terms out . we could say this is equal to negative 6 over negative 3 plus or minus the square root of 39 over negative 3 . now , this is just a 2 right here , right ?
on the second quadratic formula , for the radical negative 84 could n't you use the imaginary number ( radical negative 1 ) and multiply them together to keep on solving it ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
you would get x plus -- sorry it 's not negative -- 21 is equal to 0 . there should be a 0 there . so you get x plus 7 is equal to 0 , or x minus 3 is equal to 0 . x could be equal to negative 7 or x could be equal to 3 .
what if you have an equation such as x^2-6x=0 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
and the reason why it 's not giving you an answer , at least an answer that you might want , is because this will have no real solutions . in the future , we 're going to introduce something called an imaginary number , which is a square root of a negative number , and then we can actually express this in terms of thos...
what do sal mean by imaginary number 's ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
that 's 2 times 39 . so the square root of 156 is equal to the square root of 2 times 2 times 39 or we could say that 's the square root of 2 times 2 times the square root of 39 . and this , obviously , is just going to be the square root of 4 or this is the square root of 2 times 2 is just 2 .
he had -84 which is not a square root ( perfect square ) but could he leave the situation as -6+square root of -84/6 which would equal no solution ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ?
if b is negative in the original equation would it be positive in the formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
why is the quadratic formula so long ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ?
why did n't sal take out the negative number in the last example before working out the question ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
now , this is just a 2 right here , right ? these cancel out , 6 divided by 3 is 2 , so we get 2 . and now notice , if this is plus and we use this minus sign , the plus will become negative and the negative will become positive .
starting when you divide the numerator and denominator by 2 you get -6 so when you re wrote it you got -6 plus/minus sqrt of 39 ... but what happened to the 2 in front of the sqrt of 39 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
let 's rewrite the formula again , just in case we have n't had it memorized yet . x is going to be equal to negative b plus or minus the square root of b squared minus 4ac , all of that over 2a . i 'll supply this to another problem .
but how would you change ax^2+bx+c=0 into x equals -b plus or minus the square root of b squared minus 4c over 2a ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so that tells us that x could be equal to negative 2 plus 5 , which is 3 , or x could be equal to negative 2 minus 5 , which is negative 7 . so the quadratic formula seems to have given us an answer for this . you can verify just by substituting back in that these do work , or you could even just try to factor this rig...
so using the quadratic formula helps us find the x-intercepts , right ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
a little bit more than 6 divided by 2 is a little bit more than 2 . so you 're going to get one value that 's a little bit more than 4 and then another value that should be a little bit less than 1 . and that looks like the case , you have 1 , 2 , 3 , 4 .
but how do you find the y-intercept ( i heard that the c value is actually the y-intercept , but i 'm just making sure ) and how do you get the vertex of the graph ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
how do you use the quadratic formula in a word problem with no equation and just random numbers ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so we get x is equal to negative 6 plus or minus the square root of 36 minus -- this is interesting -- minus 4 times 3 times 10 . so this is minus -- 4 times 3 times 10 . so this is minus 120 .
how did you get the 10 in -4+ or -10 over 2 ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so that tells us that x could be equal to negative 2 plus 5 , which is 3 , or x could be equal to negative 2 minus 5 , which is negative 7 . so the quadratic formula seems to have given us an answer for this . you can verify just by substituting back in that these do work , or you could even just try to factor this rig...
the ac and p of a firm are given find quaintity sold and price charged by the firm where profits are maximum ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so that tells us that x could be equal to negative 2 plus 5 , which is 3 , or x could be equal to negative 2 minus 5 , which is negative 7 . so the quadratic formula seems to have given us an answer for this . you can verify just by substituting back in that these do work , or you could even just try to factor this rig...
what are supposed to do if the quadratic given equals x ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
you say what two numbers when you take their product , you get negative 21 and when you take their sum you get positive 4 ? so you 'd get x plus 7 times x minus 3 is equal to negative 21 . notice 7 times negative 3 is negative 21 , 7 minus 3 is positive 4 .
what are you suppose to do when the quadratic equals x ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ?
what if ( b ) is already a negative number ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
what is a real-life situation where someone would need to know the quadratic formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get 3x squared plus the 6x plus 10 is equal to 0 . and now we can use a quadratic formula . so let 's apply it here .
what is a realistic occasion where one would need to know the quadratic formula ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
so that 's the equation and we 're going to see where it intersects the x-axis . where does it equal 0 ? so let me graph it .
what is the answer of p square-7p+12=0 using factoring method ?
in this video , i 'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics . and if you 've seen many of my videos , you know that i 'm not a big fan of memorizing things . but i will recommend you memorize it with the caveat that you also remember how to prove it , becau...
we get x , this tells us that x is going to be equal to negative b . negative b is negative 4 -- i put the negative sign in front of that -- negative b plus or minus the square root of b squared . b squared is 16 , right ?
if b= a negative number , for example ; x^2-4x+5=0 and i want to put it into the quadratic formula , which wants you to change b to a negative in the front , would i change -4 to a positive 4 because it was already negative before ?