x^2-x-0.125=0

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Solution for x^2-x-0.125=0 equation: 


Simplifying
x2 + -1x + -0.125 = 0

Reorder the terms:
-0.125 + -1x + x2 = 0

Solving
-0.125 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -1x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -1x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -1x + x2 = 0 + 0.125
-1x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-1x + x2 = 0.125

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 = 0.125 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.125 + 0.25

Combine like terms: 0.125 + 0.25 = 0.375
0.25 + -1x + x2 = 0.375

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.375

Calculate the square root of the right side: 0.612372436

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.612372436 and -0.612372436.


Subproblem 1
x + -0.5 = 0.612372436

Simplifying
x + -0.5 = 0.612372436

Reorder the terms:
-0.5 + x = 0.612372436

Solving
-0.5 + x = 0.612372436

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 = 0.612372436 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.612372436 + 0.5
x = 0.612372436 + 0.5

Combine like terms: 0.612372436 + 0.5 = 1.112372436
x = 1.112372436

Simplifying
x = 1.112372436


Subproblem 2
x + -0.5 = -0.612372436

Simplifying
x + -0.5 = -0.612372436

Reorder the terms:
-0.5 + x = -0.612372436

Solving
-0.5 + x = -0.612372436

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 = -0.612372436 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.612372436 + 0.5
x = -0.612372436 + 0.5

Combine like terms: -0.612372436 + 0.5 = -0.112372436
x = -0.112372436

Simplifying
x = -0.112372436


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.112372436, -0.112372436}

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