The product of binomial and a trinomial is x^3+3x^2-x+2x^2+6x-2.

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:

 x = -2 or x = sqrt(13)/2 - 3/2 or x = -3/2 - sqrt(13)/2

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