How do you solve $-10x^2 + 11x + 24 = 20$ using the quadratic formula?

Question

1701 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-30T02:01:17

$x_(1,2) = (11 +- sqrt(281))/20$

For a general form quadratic equation

$color(blue)(ax^2 + bx + c = 0)$

you can use the quadratic formula to determine the roots of the equation

$color(blue)(x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a))$

So, start by getting your equation into standard quadratic form. To do that, add $-20$ to both sides of the equation

$-10x^2 + 11x + 24 - 20 = color(red)(cancel(color(black)(20))) - color(red)(cancel(color(black)(20)))$

$-10x^2 + 11x + 4 = 0$

In your case, you have $a = -10$ , $b = 11$ , and $c = 4$ , which means that the quadratic formula will look like this

$x_(1,2) = (-11 +- sqrt(11^2 - 4 * (-10) * (4)))/(2 * (-10))$

$x_(1,2) = (-11 +- sqrt(281))/((-20)) = (11 +- sqrt(281))/20$

The two roots of the quadratic equation will thus be

$x_1 = (11 + sqrt(281))/(20)" "$ and $" "x_2 = (11 - sqrt(281))/20$

How do you solve -10x^2 + 11x + 24 = 20-10x^2 + 11x + 24 = 20 using the quadratic formula?