x^2+12x+31-5=0

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Solution for x^2+12x+31-5=0 equation: 


Simplifying
x2 + 12x + 31 + -5 = 0

Reorder the terms:
31 + -5 + 12x + x2 = 0

Combine like terms: 31 + -5 = 26
26 + 12x + x2 = 0

Solving
26 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + 12x + -26 + x2 = 0 + -26

Reorder the terms:
26 + -26 + 12x + x2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + 12x + x2 = 0 + -26
12x + x2 = 0 + -26

Combine like terms: 0 + -26 = -26
12x + x2 = -26

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 = -26 + 36

Reorder the terms:
36 + 12x + x2 = -26 + 36

Combine like terms: -26 + 36 = 10
36 + 12x + x2 = 10

Factor a perfect square on the left side:
(x + 6)(x + 6) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 6) equal to 3.16227766 and -3.16227766.


Subproblem 1
x + 6 = 3.16227766

Simplifying
x + 6 = 3.16227766

Reorder the terms:
6 + x = 3.16227766

Solving
6 + x = 3.16227766

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 = 3.16227766 + -6

Combine like terms: 6 + -6 = 0
0 + x = 3.16227766 + -6
x = 3.16227766 + -6

Combine like terms: 3.16227766 + -6 = -2.83772234
x = -2.83772234

Simplifying
x = -2.83772234


Subproblem 2
x + 6 = -3.16227766

Simplifying
x + 6 = -3.16227766

Reorder the terms:
6 + x = -3.16227766

Solving
6 + x = -3.16227766

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 = -3.16227766 + -6

Combine like terms: 6 + -6 = 0
0 + x = -3.16227766 + -6
x = -3.16227766 + -6

Combine like terms: -3.16227766 + -6 = -9.16227766
x = -9.16227766

Simplifying
x = -9.16227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.83772234, -9.16227766}

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