Answer:
x = -2 or x = sqrt(13)/2 - 3/2 or x = -3/2 - sqrt(13)/2
Step-by-step explanation:
Solve for x:
x^3 + 5 x^2 + 5 x - 2 = 0
The left hand side factors into a product with two terms:
(x + 2) (x^2 + 3 x - 1) = 0
Split into two equations:
x + 2 = 0 or x^2 + 3 x - 1 = 0
Subtract 2 from both sides:
x = -2 or x^2 + 3 x - 1 = 0
Add 1 to both sides:
x = -2 or x^2 + 3 x = 1
Add 9/4 to both sides:
x = -2 or x^2 + 3 x + 9/4 = 13/4
Write the left hand side as a square:
x = -2 or (x + 3/2)^2 = 13/4
Take the square root of both sides:
x = -2 or x + 3/2 = sqrt(13)/2 or x + 3/2 = -sqrt(13)/2
Subtract 3/2 from both sides:
x = -2 or x = sqrt(13)/2 - 3/2 or x + 3/2 = -sqrt(13)/2
Subtract 3/2 from both sides:
Answer: x = -2 or x = sqrt(13)/2 - 3/2 or x = -3/2 - sqrt(13)/2
