x^2+1+8x-8+12=0

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Solution for x^2+1+8x-8+12=0 equation: 


Simplifying
x2 + 1 + 8x + -8 + 12 = 0

Reorder the terms:
1 + -8 + 12 + 8x + x2 = 0

Combine like terms: 1 + -8 = -7
-7 + 12 + 8x + x2 = 0

Combine like terms: -7 + 12 = 5
5 + 8x + x2 = 0

Solving
5 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 8x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 8x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8x + x2 = 0 + -5
8x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
8x + x2 = -5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -5 + 16

Reorder the terms:
16 + 8x + x2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + 8x + x2 = 11

Factor a perfect square on the left side:
(x + 4)(x + 4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 4) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + 4 = 3.31662479

Simplifying
x + 4 = 3.31662479

Reorder the terms:
4 + x = 3.31662479

Solving
4 + x = 3.31662479

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 3.31662479 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.31662479 + -4
x = 3.31662479 + -4

Combine like terms: 3.31662479 + -4 = -0.68337521
x = -0.68337521

Simplifying
x = -0.68337521


Subproblem 2
x + 4 = -3.31662479

Simplifying
x + 4 = -3.31662479

Reorder the terms:
4 + x = -3.31662479

Solving
4 + x = -3.31662479

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -3.31662479 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.31662479 + -4
x = -3.31662479 + -4

Combine like terms: -3.31662479 + -4 = -7.31662479
x = -7.31662479

Simplifying
x = -7.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.68337521, -7.31662479}

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