Question

Help! Quadratic Formula!!
Find the exact solution of the following quadratic equation by using the Quadratic Formula

Answer 1

Often, the simplest way to solve "ax2 + bx + c = 0" for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor. But sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring. While factoring may not always be successful, the Quadratic Formula can always find the solution.

The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you to solve. The Quadratic Formula is derived from the process of completing the square, and is formally stated as:

For ax2 + bx + c = 0, the value of x is given by:





x = [ -b ± sqrt(b^2 - 4ac) ] / 2a

For the Quadratic Formula to work, you must have your equation arranged in the form "(quadratic) = 0". Also, the "2a" in the denominator of the Formula is underneath everything above, not just the square root. And it's a "2a" under there, not just a plain "2". Make sure that you are careful not to drop the square root or the "plus/minus" in the middle of your calculations, or I can guarantee that you will forget to "put them back" on your test, and you'll mess yourself up. Remember that "b2" means "the square of ALL of b, including its sign", so don't leave b2 being negative, even if b is negative, because the square of a negative is a positive.

In other words, don't be sloppy and don't try to take shortcuts, because it will only hurt you in the long run. Trust me on this!

Answer 2

\(\Large\color{blue}{ \bf \frac{-b\sqrt{b^2-4ac} }{2a} }\)

Answer 3

easy and simple to read :)

Answer 4

exactly I know the quadratic formula it's just the question itself that's confusing me

Answer 5

@student_basil @david111

Answer 6

\(\Large\color{blue}{ \bf \frac{-5± \sqrt{5^2-4(-12)(2)} }{(-12)2 }}\)

Answer 7

ok so \[-\frac{ 1 }{ 4 }, \frac{ 2 }{ 3}\]

Answer 8

Wait, what ? I am not following that....

Answer 9

\(\Large\color{blue}{ \bf \frac{-5± \sqrt{5^2-4(-12)(2)} }{(-12)2 }}\)

\(\Large\color{blue}{ \bf \frac{-5± \sqrt{25+96} }{-24 }}\)

\(\Large\color{blue}{ \bf \frac{-5± 11 }{-24 }}\)

\(\Large\color{blue}{ \bf \frac{6 }{-24 },\frac{-16 }{-24 }}\)

\(\Large\color{blue}{ \bf -\frac{1 }{4 },\frac{2 }{3 }}\)

YES !

Answer 10

Good work!

Answer 11

Thankyou!!

Answer 12

You welcome !