x^2-x=180

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Solution for x^2-x=180 equation: 


Simplifying
x2 + -1x = 180

Reorder the terms:
-1x + x2 = 180

Solving
-1x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -1x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + -1x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + -1x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + -1x + x2 = 0 + 180
-1x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
-1x + x2 = 180

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 = 180 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 180 + 0.25

Combine like terms: 180 + 0.25 = 180.25
0.25 + -1x + x2 = 180.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 180.25

Calculate the square root of the right side: 13.425721582

Break this problem into two subproblems by setting 
(x + -0.5) equal to 13.425721582 and -13.425721582.


Subproblem 1
x + -0.5 = 13.425721582

Simplifying
x + -0.5 = 13.425721582

Reorder the terms:
-0.5 + x = 13.425721582

Solving
-0.5 + x = 13.425721582

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 = 13.425721582 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 13.425721582 + 0.5
x = 13.425721582 + 0.5

Combine like terms: 13.425721582 + 0.5 = 13.925721582
x = 13.925721582

Simplifying
x = 13.925721582


Subproblem 2
x + -0.5 = -13.425721582

Simplifying
x + -0.5 = -13.425721582

Reorder the terms:
-0.5 + x = -13.425721582

Solving
-0.5 + x = -13.425721582

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 = -13.425721582 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -13.425721582 + 0.5
x = -13.425721582 + 0.5

Combine like terms: -13.425721582 + 0.5 = -12.925721582
x = -12.925721582

Simplifying
x = -12.925721582


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.925721582, -12.925721582}

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