-x^2-8x-2=x+7

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Solution for -x^2-8x-2=x+7 equation: 


Simplifying
-1x2 + -8x + -2 = x + 7

Reorder the terms:
-2 + -8x + -1x2 = x + 7

Reorder the terms:
-2 + -8x + -1x2 = 7 + x

Solving
-2 + -8x + -1x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-2 + -7 + -8x + -1x + -1x2 = 7 + x + -7 + -1x

Combine like terms: -2 + -7 = -9
-9 + -8x + -1x + -1x2 = 7 + x + -7 + -1x

Combine like terms: -8x + -1x = -9x
-9 + -9x + -1x2 = 7 + x + -7 + -1x

Reorder the terms:
-9 + -9x + -1x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-9 + -9x + -1x2 = 0 + x + -1x
-9 + -9x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
-9 + -9x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 9x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(9 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
9 + 9x + x2 = 0

Solving
9 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 9x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 9x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 9x + x2 = 0 + -9
9x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
9x + x2 = -9

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -9 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -9 + 20.25

Combine like terms: -9 + 20.25 = 11.25
20.25 + 9x + x2 = 11.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 4.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + 4.5 = 3.354101966

Simplifying
x + 4.5 = 3.354101966

Reorder the terms:
4.5 + x = 3.354101966

Solving
4.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 3.354101966 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 3.354101966 + -4.5
x = 3.354101966 + -4.5

Combine like terms: 3.354101966 + -4.5 = -1.145898034
x = -1.145898034

Simplifying
x = -1.145898034


Subproblem 2
x + 4.5 = -3.354101966

Simplifying
x + 4.5 = -3.354101966

Reorder the terms:
4.5 + x = -3.354101966

Solving
4.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -3.354101966 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -3.354101966 + -4.5
x = -3.354101966 + -4.5

Combine like terms: -3.354101966 + -4.5 = -7.854101966
x = -7.854101966

Simplifying
x = -7.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.145898034, -7.854101966}
Solution
x = {-1.145898034, -7.854101966}

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