-4x^2-24x-24=0 Please Help!

Question

I need to figure out how to solve by graphing, factoring, completing the square, and the quadratic formula. Please help!

Answer 1

First of all this is an equation; make it simple by dividing by -4 so that you have

x²+6x+6=0.

The only possible rational roots are 1,2,3,6 and the negatives of those choices. It is easy to rule out all of the choices.

The graph is a parabola with vertex at x=-3.

(x+3)² = x² + 6x + 9; therefore your original equation converts to

(x+3)² - 3 = 0 (This is "completing the square)

and your roots are -3±√3.

The roots from the quadratic formula are [-6 ± sqrt(36-24)]/2.