Question

Determine the solutions to the quadratic equation -4x2 - 32x - 64 = 0.

Answer 1

-4x^2 - 32x - 64 = 0
-4 (x^2 + 8x + 16) = 0
-4 (x +4)(x+4) = 0
x+ 4 =0
x = -4

Answer 2

Factor out -4:

-4(x^2 + 8x + 16) = 0

We can take out the -4 by dividing both sides by -4 since we don't really need it to find the roots. So we get:

x^2 + 8x + 16 = 0

Now we factor the quadratic. To do that we need to find two numbers which multiply to 16 and add up to 8. Such two numbers are 4 and 4.

(x + 4)(x + 4) = (x + 4)^2 = 0

Can you find which x-value would satisfy the equation now that we have factored?

@amandaschlor