Question

Which of the following are solutions to the equation below?

Check all that apply.
3x2 + 27x + 54 = 0

A.9
B.-6
C.6
D.3
E.3

Answer 1

x = -3 or x = -6

Explanation:

Solve for x over the real numbers:

3 x^2 + 27 x + 54 = 0

The left hand side factors into a product with three terms:

3 (x + 3) (x + 6) = 0

Divide both sides by 3:

(x + 3) (x + 6) = 0

Split into two equations:

x + 3 = 0 or x + 6 = 0

Subtract 3 from both sides:

x = -3 or x + 6 = 0

Subtract 6 from both sides:

Answer: x = -3 or x = -6

Answer 2

x = -3, -6.

Explanation:

3x2 + 27x + 54 = 0

Divide through by 3:

x^2 + 9x + 18 = 0

(x + 3)(x + 6) = 0

x = -3, -6.