2x^2-26x-126=0

Solution for 2x^2-26x-126=0 equation:

Simplifying
2x2 + -26x + -126 = 0

Reorder the terms:
-126 + -26x + 2x2 = 0

Solving
-126 + -26x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-63 + -13x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-63 + -13x + x2)' equal to zero and attempt to solve:

Simplifying
-63 + -13x + x2 = 0

Solving
-63 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '63' to each side of the equation.
-63 + -13x + 63 + x2 = 0 + 63

Reorder the terms:
-63 + 63 + -13x + x2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + -13x + x2 = 0 + 63
-13x + x2 = 0 + 63

Combine like terms: 0 + 63 = 63
-13x + x2 = 63

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 = 63 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 63 + 42.25

Combine like terms: 63 + 42.25 = 105.25
42.25 + -13x + x2 = 105.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 105.25

Calculate the square root of the right side: 10.259142264

Break this problem into two subproblems by setting 
(x + -6.5) equal to 10.259142264 and -10.259142264.

Subproblem 1
x + -6.5 = 10.259142264

Simplifying
x + -6.5 = 10.259142264

Reorder the terms:
-6.5 + x = 10.259142264

Solving
-6.5 + x = 10.259142264

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 = 10.259142264 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 10.259142264 + 6.5
x = 10.259142264 + 6.5

Combine like terms: 10.259142264 + 6.5 = 16.759142264
x = 16.759142264

Simplifying
x = 16.759142264

Subproblem 2
x + -6.5 = -10.259142264

Simplifying
x + -6.5 = -10.259142264

Reorder the terms:
-6.5 + x = -10.259142264

Solving
-6.5 + x = -10.259142264

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 = -10.259142264 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -10.259142264 + 6.5
x = -10.259142264 + 6.5

Combine like terms: -10.259142264 + 6.5 = -3.759142264
x = -3.759142264

Simplifying
x = -3.759142264

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.759142264, -3.759142264}
Solution
x = {16.759142264, -3.759142264}