2x^2-2x-112=100

Solution for 2x^2-2x-112=100 equation:

Simplifying
2x2 + -2x + -112 = 100

Reorder the terms:
-112 + -2x + 2x2 = 100

Solving
-112 + -2x + 2x2 = 100

Solving for variable 'x'.

Reorder the terms:
-112 + -100 + -2x + 2x2 = 100 + -100

Combine like terms: -112 + -100 = -212
-212 + -2x + 2x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-212 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-106 + -1x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-106 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-106 + -1x + x2 = 0

Solving
-106 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '106' to each side of the equation.
-106 + -1x + 106 + x2 = 0 + 106

Reorder the terms:
-106 + 106 + -1x + x2 = 0 + 106

Combine like terms: -106 + 106 = 0
0 + -1x + x2 = 0 + 106
-1x + x2 = 0 + 106

Combine like terms: 0 + 106 = 106
-1x + x2 = 106

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 = 106 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 106 + 0.25

Combine like terms: 106 + 0.25 = 106.25
0.25 + -1x + x2 = 106.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(x + -0.5) equal to 10.307764064 and -10.307764064.

Subproblem 1
x + -0.5 = 10.307764064

Simplifying
x + -0.5 = 10.307764064

Reorder the terms:
-0.5 + x = 10.307764064

Solving
-0.5 + x = 10.307764064

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 = 10.307764064 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 10.307764064 + 0.5
x = 10.307764064 + 0.5

Combine like terms: 10.307764064 + 0.5 = 10.807764064
x = 10.807764064

Simplifying
x = 10.807764064

Subproblem 2
x + -0.5 = -10.307764064

Simplifying
x + -0.5 = -10.307764064

Reorder the terms:
-0.5 + x = -10.307764064

Solving
-0.5 + x = -10.307764064

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 = -10.307764064 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -10.307764064 + 0.5
x = -10.307764064 + 0.5

Combine like terms: -10.307764064 + 0.5 = -9.807764064
x = -9.807764064

Simplifying
x = -9.807764064

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.807764064, -9.807764064}
Solution
x = {10.807764064, -9.807764064}