4x^2+52x-52=0

Solution for 4x^2+52x-52=0 equation:

Simplifying
4x2 + 52x + -52 = 0

Reorder the terms:
-52 + 52x + 4x2 = 0

Solving
-52 + 52x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-13 + 13x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-13 + 13x + x2)' equal to zero and attempt to solve:

Simplifying
-13 + 13x + x2 = 0

Solving
-13 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 13x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + 13x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 13x + x2 = 0 + 13
13x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
13x + x2 = 13

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 13 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 13 + 42.25

Combine like terms: 13 + 42.25 = 55.25
42.25 + 13x + x2 = 55.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 55.25

Calculate the square root of the right side: 7.433034374

Break this problem into two subproblems by setting 
(x + 6.5) equal to 7.433034374 and -7.433034374.

Subproblem 1
x + 6.5 = 7.433034374

Simplifying
x + 6.5 = 7.433034374

Reorder the terms:
6.5 + x = 7.433034374

Solving
6.5 + x = 7.433034374

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 7.433034374 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 7.433034374 + -6.5
x = 7.433034374 + -6.5

Combine like terms: 7.433034374 + -6.5 = 0.933034374
x = 0.933034374

Simplifying
x = 0.933034374

Subproblem 2
x + 6.5 = -7.433034374

Simplifying
x + 6.5 = -7.433034374

Reorder the terms:
6.5 + x = -7.433034374

Solving
6.5 + x = -7.433034374

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -7.433034374 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -7.433034374 + -6.5
x = -7.433034374 + -6.5

Combine like terms: -7.433034374 + -6.5 = -13.933034374
x = -13.933034374

Simplifying
x = -13.933034374

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.933034374, -13.933034374}
Solution
x = {0.933034374, -13.933034374}