x^2-x-182.5=0

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Solution for x^2-x-182.5=0 equation: 


Simplifying
x2 + -1x + -182.5 = 0

Reorder the terms:
-182.5 + -1x + x2 = 0

Solving
-182.5 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '182.5' to each side of the equation.
-182.5 + -1x + 182.5 + x2 = 0 + 182.5

Reorder the terms:
-182.5 + 182.5 + -1x + x2 = 0 + 182.5

Combine like terms: -182.5 + 182.5 = 0.0
0.0 + -1x + x2 = 0 + 182.5
-1x + x2 = 0 + 182.5

Combine like terms: 0 + 182.5 = 182.5
-1x + x2 = 182.5

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 = 182.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 182.5 + 0.25

Combine like terms: 182.5 + 0.25 = 182.75
0.25 + -1x + x2 = 182.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 182.75

Calculate the square root of the right side: 13.518505835

Break this problem into two subproblems by setting 
(x + -0.5) equal to 13.518505835 and -13.518505835.


Subproblem 1
x + -0.5 = 13.518505835

Simplifying
x + -0.5 = 13.518505835

Reorder the terms:
-0.5 + x = 13.518505835

Solving
-0.5 + x = 13.518505835

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 = 13.518505835 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 13.518505835 + 0.5
x = 13.518505835 + 0.5

Combine like terms: 13.518505835 + 0.5 = 14.018505835
x = 14.018505835

Simplifying
x = 14.018505835


Subproblem 2
x + -0.5 = -13.518505835

Simplifying
x + -0.5 = -13.518505835

Reorder the terms:
-0.5 + x = -13.518505835

Solving
-0.5 + x = -13.518505835

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 = -13.518505835 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -13.518505835 + 0.5
x = -13.518505835 + 0.5

Combine like terms: -13.518505835 + 0.5 = -13.018505835
x = -13.018505835

Simplifying
x = -13.018505835


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.018505835, -13.018505835}

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