x^2-x=780.25

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Solution for x^2-x=780.25 equation: 


Simplifying
x2 + -1x = 780.25

Reorder the terms:
-1x + x2 = 780.25

Solving
-1x + x2 = 780.25

Solving for variable 'x'.

Reorder the terms:
-780.25 + -1x + x2 = 780.25 + -780.25

Combine like terms: 780.25 + -780.25 = 0.00
-780.25 + -1x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '780.25' to each side of the equation.
-780.25 + -1x + 780.25 + x2 = 0.00 + 780.25

Reorder the terms:
-780.25 + 780.25 + -1x + x2 = 0.00 + 780.25

Combine like terms: -780.25 + 780.25 = 0.00
0.00 + -1x + x2 = 0.00 + 780.25
-1x + x2 = 0.00 + 780.25

Combine like terms: 0.00 + 780.25 = 780.25
-1x + x2 = 780.25

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 = 780.25 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 780.25 + 0.25

Combine like terms: 780.25 + 0.25 = 780.5
0.25 + -1x + x2 = 780.5

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 780.5

Calculate the square root of the right side: 27.937430089

Break this problem into two subproblems by setting 
(x + -0.5) equal to 27.937430089 and -27.937430089.


Subproblem 1
x + -0.5 = 27.937430089

Simplifying
x + -0.5 = 27.937430089

Reorder the terms:
-0.5 + x = 27.937430089

Solving
-0.5 + x = 27.937430089

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 = 27.937430089 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 27.937430089 + 0.5
x = 27.937430089 + 0.5

Combine like terms: 27.937430089 + 0.5 = 28.437430089
x = 28.437430089

Simplifying
x = 28.437430089


Subproblem 2
x + -0.5 = -27.937430089

Simplifying
x + -0.5 = -27.937430089

Reorder the terms:
-0.5 + x = -27.937430089

Solving
-0.5 + x = -27.937430089

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 = -27.937430089 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -27.937430089 + 0.5
x = -27.937430089 + 0.5

Combine like terms: -27.937430089 + 0.5 = -27.437430089
x = -27.437430089

Simplifying
x = -27.437430089


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.437430089, -27.437430089}

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