8x^2+8x-220=0

Solution for 8x^2+8x-220=0 equation:

Simplifying
8x2 + 8x + -220 = 0

Reorder the terms:
-220 + 8x + 8x2 = 0

Solving
-220 + 8x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-55 + 2x + 2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-55 + 2x + 2x2)' equal to zero and attempt to solve:

Simplifying
-55 + 2x + 2x2 = 0

Solving
-55 + 2x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-27.5 + x + x2 = 0

Move the constant term to the right:

Add '27.5' to each side of the equation.
-27.5 + x + 27.5 + x2 = 0 + 27.5

Reorder the terms:
-27.5 + 27.5 + x + x2 = 0 + 27.5

Combine like terms: -27.5 + 27.5 = 0.0
0.0 + x + x2 = 0 + 27.5
x + x2 = 0 + 27.5

Combine like terms: 0 + 27.5 = 27.5
x + x2 = 27.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 27.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 27.5 + 0.25

Combine like terms: 27.5 + 0.25 = 27.75
1.25 + x2 = 27.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 27.75

Calculate the square root of the right side: 5.267826876

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.267826876 and -5.267826876.

Subproblem 1
x + 0.5 = 5.267826876

Simplifying
x + 0.5 = 5.267826876

Reorder the terms:
0.5 + x = 5.267826876

Solving
0.5 + x = 5.267826876

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 5.267826876 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.267826876 + -0.5
x = 5.267826876 + -0.5

Combine like terms: 5.267826876 + -0.5 = 4.767826876
x = 4.767826876

Simplifying
x = 4.767826876

Subproblem 2
x + 0.5 = -5.267826876

Simplifying
x + 0.5 = -5.267826876

Reorder the terms:
0.5 + x = -5.267826876

Solving
0.5 + x = -5.267826876

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -5.267826876 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.267826876 + -0.5
x = -5.267826876 + -0.5

Combine like terms: -5.267826876 + -0.5 = -5.767826876
x = -5.767826876

Simplifying
x = -5.767826876

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.767826876, -5.767826876}
Solution
x = {4.767826876, -5.767826876}