Solve for x: by completing the square:
x^3 + 7 x^2 - 12 x - 18 = 0
The left hand side factors into a product with two terms:
(x + 1) (x^2 + 6 x - 18) = 0
Split into two equations:
x + 1 = 0 or x^2 + 6 x - 18 = 0
Subtract 1 from both sides:
x = -1 or x^2 + 6 x - 18 = 0
Add 18 to both sides:
x = -1 or x^2 + 6 x = 18
Add 9 to both sides:
x = -1 or x^2 + 6 x + 9 = 27
Write the left hand side as a square:
x = -1 or (x + 3)^2 = 27
Take the square root of both sides:
x = -1 or x + 3 = 3 sqrt(3) or x + 3 = -3 sqrt(3)
Subtract 3 from both sides:
x = -1 or x = 3 sqrt(3) - 3 or x + 3 = -3 sqrt(3)
Subtract 3 from both sides:
Answer: x = -1 or x = 3 sqrt(3) - 3 or x = -3 - 3 sqrt(3)
