x^2-x=12.5

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Solution for x^2-x=12.5 equation: 


Simplifying
x2 + -1x = 12.5

Reorder the terms:
-1x + x2 = 12.5

Solving
-1x + x2 = 12.5

Solving for variable 'x'.

Reorder the terms:
-12.5 + -1x + x2 = 12.5 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
-12.5 + -1x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -1x + 12.5 + x2 = 0.0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -1x + x2 = 0.0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -1x + x2 = 0.0 + 12.5
-1x + x2 = 0.0 + 12.5

Combine like terms: 0.0 + 12.5 = 12.5
-1x + x2 = 12.5

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 = 12.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 12.5 + 0.25

Combine like terms: 12.5 + 0.25 = 12.75
0.25 + -1x + x2 = 12.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 12.75

Calculate the square root of the right side: 3.570714214

Break this problem into two subproblems by setting 
(x + -0.5) equal to 3.570714214 and -3.570714214.


Subproblem 1
x + -0.5 = 3.570714214

Simplifying
x + -0.5 = 3.570714214

Reorder the terms:
-0.5 + x = 3.570714214

Solving
-0.5 + x = 3.570714214

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 = 3.570714214 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 3.570714214 + 0.5
x = 3.570714214 + 0.5

Combine like terms: 3.570714214 + 0.5 = 4.070714214
x = 4.070714214

Simplifying
x = 4.070714214


Subproblem 2
x + -0.5 = -3.570714214

Simplifying
x + -0.5 = -3.570714214

Reorder the terms:
-0.5 + x = -3.570714214

Solving
-0.5 + x = -3.570714214

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 = -3.570714214 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -3.570714214 + 0.5
x = -3.570714214 + 0.5

Combine like terms: -3.570714214 + 0.5 = -3.070714214
x = -3.070714214

Simplifying
x = -3.070714214


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.070714214, -3.070714214}

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