x(x-1)=66

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Solution for x(x-1)=66 equation:


Simplifying
x(x + -1) = 66

Reorder the terms:
x(-1 + x) = 66
(-1 * x + x * x) = 66
(-1x + x2) = 66

Solving
-1x + x2 = 66

Solving for variable 'x'.

Reorder the terms:
-66 + -1x + x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + -1x + 66 + x2 = 0 + 66

Reorder the terms:
-66 + 66 + -1x + x2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + -1x + x2 = 0 + 66
-1x + x2 = 0 + 66

Combine like terms: 0 + 66 = 66
-1x + x2 = 66

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 = 66 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 66 + 0.25

Combine like terms: 66 + 0.25 = 66.25
0.25 + -1x + x2 = 66.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(x + -0.5) equal to 8.139410298 and -8.139410298.


Subproblem 1
x + -0.5 = 8.139410298

Simplifying
x + -0.5 = 8.139410298

Reorder the terms:
-0.5 + x = 8.139410298

Solving
-0.5 + x = 8.139410298

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 = 8.139410298 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 8.139410298 + 0.5
x = 8.139410298 + 0.5

Combine like terms: 8.139410298 + 0.5 = 8.639410298
x = 8.639410298

Simplifying
x = 8.639410298


Subproblem 2
x + -0.5 = -8.139410298

Simplifying
x + -0.5 = -8.139410298

Reorder the terms:
-0.5 + x = -8.139410298

Solving
-0.5 + x = -8.139410298

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 = -8.139410298 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -8.139410298 + 0.5
x = -8.139410298 + 0.5

Combine like terms: -8.139410298 + 0.5 = -7.639410298
x = -7.639410298

Simplifying
x = -7.639410298


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.639410298, -7.639410298}

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