x^2+12x+32=4

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Solution for x^2+12x+32=4 equation: 


Simplifying
x2 + 12x + 32 = 4

Reorder the terms:
32 + 12x + x2 = 4

Solving
32 + 12x + x2 = 4

Solving for variable 'x'.

Reorder the terms:
32 + -4 + 12x + x2 = 4 + -4

Combine like terms: 32 + -4 = 28
28 + 12x + x2 = 4 + -4

Combine like terms: 4 + -4 = 0
28 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + 12x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + 12x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + 12x + x2 = 0 + -28
12x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
12x + x2 = -28

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 = -28 + 36

Reorder the terms:
36 + 12x + x2 = -28 + 36

Combine like terms: -28 + 36 = 8
36 + 12x + x2 = 8

Factor a perfect square on the left side:
(x + 6)(x + 6) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + 6) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + 6 = 2.828427125

Simplifying
x + 6 = 2.828427125

Reorder the terms:
6 + x = 2.828427125

Solving
6 + x = 2.828427125

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 = 2.828427125 + -6

Combine like terms: 6 + -6 = 0
0 + x = 2.828427125 + -6
x = 2.828427125 + -6

Combine like terms: 2.828427125 + -6 = -3.171572875
x = -3.171572875

Simplifying
x = -3.171572875


Subproblem 2
x + 6 = -2.828427125

Simplifying
x + 6 = -2.828427125

Reorder the terms:
6 + x = -2.828427125

Solving
6 + x = -2.828427125

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 = -2.828427125 + -6

Combine like terms: 6 + -6 = 0
0 + x = -2.828427125 + -6
x = -2.828427125 + -6

Combine like terms: -2.828427125 + -6 = -8.828427125
x = -8.828427125

Simplifying
x = -8.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.171572875, -8.828427125}

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