(x-5)=(x^2-2x-6)

Solution for (x-5)=(x^2-2x-6) equation:

Simplifying
(x + -5) = (x2 + -2x + -6)

Reorder the terms:
(-5 + x) = (x2 + -2x + -6)

Remove parenthesis around (-5 + x)
-5 + x = (x2 + -2x + -6)

Reorder the terms:
-5 + x = (-6 + -2x + x2)

Remove parenthesis around (-6 + -2x + x2)
-5 + x = -6 + -2x + x2

Solving
-5 + x = -6 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-5 + 6 + x + 2x + -1x2 = -6 + -2x + x2 + 6 + 2x + -1x2

Combine like terms: -5 + 6 = 1
1 + x + 2x + -1x2 = -6 + -2x + x2 + 6 + 2x + -1x2

Combine like terms: x + 2x = 3x
1 + 3x + -1x2 = -6 + -2x + x2 + 6 + 2x + -1x2

Reorder the terms:
1 + 3x + -1x2 = -6 + 6 + -2x + 2x + x2 + -1x2

Combine like terms: -6 + 6 = 0
1 + 3x + -1x2 = 0 + -2x + 2x + x2 + -1x2
1 + 3x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
1 + 3x + -1x2 = 0 + x2 + -1x2
1 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -3x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -3x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x + x2 = 0 + 1
-3x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3x + x2 = 1

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 1 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + -3x + x2 = 3.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + -1.5 = 1.802775638

Simplifying
x + -1.5 = 1.802775638

Reorder the terms:
-1.5 + x = 1.802775638

Solving
-1.5 + x = 1.802775638

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.802775638 + 1.5
x = 1.802775638 + 1.5

Combine like terms: 1.802775638 + 1.5 = 3.302775638
x = 3.302775638

Simplifying
x = 3.302775638

Subproblem 2
x + -1.5 = -1.802775638

Simplifying
x + -1.5 = -1.802775638

Reorder the terms:
-1.5 + x = -1.802775638

Solving
-1.5 + x = -1.802775638

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.802775638 + 1.5
x = -1.802775638 + 1.5

Combine like terms: -1.802775638 + 1.5 = -0.302775638
x = -0.302775638

Simplifying
x = -0.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.302775638, -0.302775638}