Question

Solve for x:
4x² + 36x = - 120

Answer 1

First, we can simplify the equation by dividing both sides by 4:

x² + 9x = -30

Next, we can complete the square to solve for x:

x² + 9x + (9/2)² = -30 + (9/2)²

(x + (9/2))² = -120/4 + 81/4

(x + (9/2))² = -39/4

x + (9/2) = ±√(-39/4)

x = (-9 ± √39i)/2

Therefore, the solutions for x are x = (-9 + √39i)/2 and x = (-9 - √39i)/2.

Answer 2

First, get all the term to one side:

4x^2 + 36x + 120 = 0

Then, factor out the greatest common factor of the terms.

4(x^2 + 9x + 30) = 0

Next, this trinomial is not factorable, so you need to use the quadratic formula:

(-9 +- sqrt(81 -4(1)(30))) / 2(1)

Both solutions to this quadratic are imaginary

x = (-9 + isqrt(39)) / 2
x = (-9 - isqrt(39)) / 2