x^2-6x-8=6x+8

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Solution for x^2-6x-8=6x+8 equation:


Simplifying
x2 + -6x + -8 = 6x + 8

Reorder the terms:
-8 + -6x + x2 = 6x + 8

Reorder the terms:
-8 + -6x + x2 = 8 + 6x

Solving
-8 + -6x + x2 = 8 + 6x

Solving for variable 'x'.

Reorder the terms:
-8 + -8 + -6x + -6x + x2 = 8 + 6x + -8 + -6x

Combine like terms: -8 + -8 = -16
-16 + -6x + -6x + x2 = 8 + 6x + -8 + -6x

Combine like terms: -6x + -6x = -12x
-16 + -12x + x2 = 8 + 6x + -8 + -6x

Reorder the terms:
-16 + -12x + x2 = 8 + -8 + 6x + -6x

Combine like terms: 8 + -8 = 0
-16 + -12x + x2 = 0 + 6x + -6x
-16 + -12x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-16 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -12x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -12x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -12x + x2 = 0 + 16
-12x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-12x + x2 = 16

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 16 + 36

Reorder the terms:
36 + -12x + x2 = 16 + 36

Combine like terms: 16 + 36 = 52
36 + -12x + x2 = 52

Factor a perfect square on the left side:
(x + -6)(x + -6) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + -6) equal to 7.211102551 and -7.211102551.

Subproblem 1

x + -6 = 7.211102551 Simplifying x + -6 = 7.211102551 Reorder the terms: -6 + x = 7.211102551 Solving -6 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.211102551 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.211102551 + 6 x = 7.211102551 + 6 Combine like terms: 7.211102551 + 6 = 13.211102551 x = 13.211102551 Simplifying x = 13.211102551

Subproblem 2

x + -6 = -7.211102551 Simplifying x + -6 = -7.211102551 Reorder the terms: -6 + x = -7.211102551 Solving -6 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.211102551 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.211102551 + 6 x = -7.211102551 + 6 Combine like terms: -7.211102551 + 6 = -1.211102551 x = -1.211102551 Simplifying x = -1.211102551

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.211102551, -1.211102551}

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