2(x^2-x-112)=0

Solution for 2(x^2-x-112)=0 equation:

Simplifying
2(x2 + -1x + -112) = 0

Reorder the terms:
2(-112 + -1x + x2) = 0
(-112 * 2 + -1x * 2 + x2 * 2) = 0
(-224 + -2x + 2x2) = 0

Solving
-224 + -2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-112 + -1x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-112 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-112 + -1x + x2 = 0

Solving
-112 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '112' to each side of the equation.
-112 + -1x + 112 + x2 = 0 + 112

Reorder the terms:
-112 + 112 + -1x + x2 = 0 + 112

Combine like terms: -112 + 112 = 0
0 + -1x + x2 = 0 + 112
-1x + x2 = 0 + 112

Combine like terms: 0 + 112 = 112
-1x + x2 = 112

The x term is -1x.  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.
-1x + 0.25 + x2 = 112 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 112 + 0.25

Combine like terms: 112 + 0.25 = 112.25
0.25 + -1x + x2 = 112.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 112.25

Calculate the square root of the right side: 10.59481005

Break this problem into two subproblems by setting 
(x + -0.5) equal to 10.59481005 and -10.59481005.

Subproblem 1
x + -0.5 = 10.59481005

Simplifying
x + -0.5 = 10.59481005

Reorder the terms:
-0.5 + x = 10.59481005

Solving
-0.5 + x = 10.59481005

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 = 10.59481005 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 10.59481005 + 0.5
x = 10.59481005 + 0.5

Combine like terms: 10.59481005 + 0.5 = 11.09481005
x = 11.09481005

Simplifying
x = 11.09481005

Subproblem 2
x + -0.5 = -10.59481005

Simplifying
x + -0.5 = -10.59481005

Reorder the terms:
-0.5 + x = -10.59481005

Solving
-0.5 + x = -10.59481005

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 = -10.59481005 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -10.59481005 + 0.5
x = -10.59481005 + 0.5

Combine like terms: -10.59481005 + 0.5 = -10.09481005
x = -10.09481005

Simplifying
x = -10.09481005

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.09481005, -10.09481005}
Solution
x = {11.09481005, -10.09481005}