-2x^2-12x=2x-8

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Solution for -2x^2-12x=2x-8 equation: 


Simplifying
-2x2 + -12x = 2x + -8

Reorder the terms:
-12x + -2x2 = 2x + -8

Reorder the terms:
-12x + -2x2 = -8 + 2x

Solving
-12x + -2x2 = -8 + 2x

Solving for variable 'x'.

Reorder the terms:
8 + -12x + -2x + -2x2 = -8 + 2x + 8 + -2x

Combine like terms: -12x + -2x = -14x
8 + -14x + -2x2 = -8 + 2x + 8 + -2x

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

Combine like terms: -8 + 8 = 0
8 + -14x + -2x2 = 0 + 2x + -2x
8 + -14x + -2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
8 + -14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -7x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -7x + -1x2)' equal to zero and attempt to solve:

Simplifying
4 + -7x + -1x2 = 0

Solving
4 + -7x + -1x2 = 0

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

Divide each side by '-1'.
-4 + 7x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 7x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 7x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 7x + x2 = 0 + 4
7x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
7x + x2 = 4

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 4 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 4 + 12.25

Combine like terms: 4 + 12.25 = 16.25
12.25 + 7x + x2 = 16.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.031128874 and -4.031128874.


Subproblem 1
x + 3.5 = 4.031128874

Simplifying
x + 3.5 = 4.031128874

Reorder the terms:
3.5 + x = 4.031128874

Solving
3.5 + x = 4.031128874

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 4.031128874 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.031128874 + -3.5
x = 4.031128874 + -3.5

Combine like terms: 4.031128874 + -3.5 = 0.531128874
x = 0.531128874

Simplifying
x = 0.531128874


Subproblem 2
x + 3.5 = -4.031128874

Simplifying
x + 3.5 = -4.031128874

Reorder the terms:
3.5 + x = -4.031128874

Solving
3.5 + x = -4.031128874

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -4.031128874 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.031128874 + -3.5
x = -4.031128874 + -3.5

Combine like terms: -4.031128874 + -3.5 = -7.531128874
x = -7.531128874

Simplifying
x = -7.531128874


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.531128874, -7.531128874}
Solution
x = {0.531128874, -7.531128874}

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