x^2-2x-8=2x+14

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Solution for x^2-2x-8=2x+14 equation:


Simplifying
x2 + -2x + -8 = 2x + 14

Reorder the terms:
-8 + -2x + x2 = 2x + 14

Reorder the terms:
-8 + -2x + x2 = 14 + 2x

Solving
-8 + -2x + x2 = 14 + 2x

Solving for variable 'x'.

Reorder the terms:
-8 + -14 + -2x + -2x + x2 = 14 + 2x + -14 + -2x

Combine like terms: -8 + -14 = -22
-22 + -2x + -2x + x2 = 14 + 2x + -14 + -2x

Combine like terms: -2x + -2x = -4x
-22 + -4x + x2 = 14 + 2x + -14 + -2x

Reorder the terms:
-22 + -4x + x2 = 14 + -14 + 2x + -2x

Combine like terms: 14 + -14 = 0
-22 + -4x + x2 = 0 + 2x + -2x
-22 + -4x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-22 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -4x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + -4x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -4x + x2 = 0 + 22
-4x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
-4x + x2 = 22

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 22 + 4

Reorder the terms:
4 + -4x + x2 = 22 + 4

Combine like terms: 22 + 4 = 26
4 + -4x + x2 = 26

Factor a perfect square on the left side:
(x + -2)(x + -2) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + -2) equal to 5.099019514 and -5.099019514.


Subproblem 1
x + -2 = 5.099019514

Simplifying
x + -2 = 5.099019514

Reorder the terms:
-2 + x = 5.099019514

Solving
-2 + x = 5.099019514

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 5.099019514 + 2

Combine like terms: -2 + 2 = 0
0 + x = 5.099019514 + 2
x = 5.099019514 + 2

Combine like terms: 5.099019514 + 2 = 7.099019514
x = 7.099019514

Simplifying
x = 7.099019514


Subproblem 2
x + -2 = -5.099019514

Simplifying
x + -2 = -5.099019514

Reorder the terms:
-2 + x = -5.099019514

Solving
-2 + x = -5.099019514

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -5.099019514 + 2

Combine like terms: -2 + 2 = 0
0 + x = -5.099019514 + 2
x = -5.099019514 + 2

Combine like terms: -5.099019514 + 2 = -3.099019514
x = -3.099019514

Simplifying
x = -3.099019514


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.099019514, -3.099019514}

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