x^2-x=10.64

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Solution for x^2-x=10.64 equation: 


Simplifying
x2 + -1x = 10.64

Reorder the terms:
-1x + x2 = 10.64

Solving
-1x + x2 = 10.64

Solving for variable 'x'.

Reorder the terms:
-10.64 + -1x + x2 = 10.64 + -10.64

Combine like terms: 10.64 + -10.64 = 0.00
-10.64 + -1x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '10.64' to each side of the equation.
-10.64 + -1x + 10.64 + x2 = 0.00 + 10.64

Reorder the terms:
-10.64 + 10.64 + -1x + x2 = 0.00 + 10.64

Combine like terms: -10.64 + 10.64 = 0.00
0.00 + -1x + x2 = 0.00 + 10.64
-1x + x2 = 0.00 + 10.64

Combine like terms: 0.00 + 10.64 = 10.64
-1x + x2 = 10.64

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 = 10.64 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 10.64 + 0.25

Combine like terms: 10.64 + 0.25 = 10.89
0.25 + -1x + x2 = 10.89

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 10.89

Calculate the square root of the right side: 3.3

Break this problem into two subproblems by setting 
(x + -0.5) equal to 3.3 and -3.3.


Subproblem 1
x + -0.5 = 3.3

Simplifying
x + -0.5 = 3.3

Reorder the terms:
-0.5 + x = 3.3

Solving
-0.5 + x = 3.3

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 = 3.3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 3.3 + 0.5
x = 3.3 + 0.5

Combine like terms: 3.3 + 0.5 = 3.8
x = 3.8

Simplifying
x = 3.8


Subproblem 2
x + -0.5 = -3.3

Simplifying
x + -0.5 = -3.3

Reorder the terms:
-0.5 + x = -3.3

Solving
-0.5 + x = -3.3

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 = -3.3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -3.3 + 0.5
x = -3.3 + 0.5

Combine like terms: -3.3 + 0.5 = -2.8
x = -2.8

Simplifying
x = -2.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.8, -2.8}

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