x^2-x-225=0

Solution for x^2-x-225=0 equation:

Simplifying
x2 + -1x + -225 = 0

Reorder the terms:
-225 + -1x + x2 = 0

Solving
-225 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + -1x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + -1x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + -1x + x2 = 0 + 225
-1x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
-1x + x2 = 225

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 = 225 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 225 + 0.25

Combine like terms: 225 + 0.25 = 225.25
0.25 + -1x + x2 = 225.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 225.25

Calculate the square root of the right side: 15.00833102

Break this problem into two subproblems by setting 
(x + -0.5) equal to 15.00833102 and -15.00833102.

Subproblem 1
x + -0.5 = 15.00833102

Simplifying
x + -0.5 = 15.00833102

Reorder the terms:
-0.5 + x = 15.00833102

Solving
-0.5 + x = 15.00833102

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 = 15.00833102 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 15.00833102 + 0.5
x = 15.00833102 + 0.5

Combine like terms: 15.00833102 + 0.5 = 15.50833102
x = 15.50833102

Simplifying
x = 15.50833102

Subproblem 2
x + -0.5 = -15.00833102

Simplifying
x + -0.5 = -15.00833102

Reorder the terms:
-0.5 + x = -15.00833102

Solving
-0.5 + x = -15.00833102

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 = -15.00833102 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -15.00833102 + 0.5
x = -15.00833102 + 0.5

Combine like terms: -15.00833102 + 0.5 = -14.50833102
x = -14.50833102

Simplifying
x = -14.50833102

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.50833102, -14.50833102}