x^2-x=67

Solution for x^2-x=67 equation:

Simplifying
x2 + -1x = 67

Reorder the terms:
-1x + x2 = 67

Solving
-1x + x2 = 67

Solving for variable 'x'.

Reorder the terms:
-67 + -1x + x2 = 67 + -67

Combine like terms: 67 + -67 = 0
-67 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '67' to each side of the equation.
-67 + -1x + 67 + x2 = 0 + 67

Reorder the terms:
-67 + 67 + -1x + x2 = 0 + 67

Combine like terms: -67 + 67 = 0
0 + -1x + x2 = 0 + 67
-1x + x2 = 0 + 67

Combine like terms: 0 + 67 = 67
-1x + x2 = 67

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 = 67 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 67 + 0.25

Combine like terms: 67 + 0.25 = 67.25
0.25 + -1x + x2 = 67.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 67.25

Calculate the square root of the right side: 8.200609733

Break this problem into two subproblems by setting 
(x + -0.5) equal to 8.200609733 and -8.200609733.

Subproblem 1
x + -0.5 = 8.200609733

Simplifying
x + -0.5 = 8.200609733

Reorder the terms:
-0.5 + x = 8.200609733

Solving
-0.5 + x = 8.200609733

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 = 8.200609733 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 8.200609733 + 0.5
x = 8.200609733 + 0.5

Combine like terms: 8.200609733 + 0.5 = 8.700609733
x = 8.700609733

Simplifying
x = 8.700609733

Subproblem 2
x + -0.5 = -8.200609733

Simplifying
x + -0.5 = -8.200609733

Reorder the terms:
-0.5 + x = -8.200609733

Solving
-0.5 + x = -8.200609733

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 = -8.200609733 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -8.200609733 + 0.5
x = -8.200609733 + 0.5

Combine like terms: -8.200609733 + 0.5 = -7.700609733
x = -7.700609733

Simplifying
x = -7.700609733

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.700609733, -7.700609733}