x^2+6x-31=0

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Solution for x^2+6x-31=0 equation: 


Simplifying
x2 + 6x + -31 = 0

Reorder the terms:
-31 + 6x + x2 = 0

Solving
-31 + 6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 6x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + 6x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 6x + x2 = 0 + 31
6x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
6x + x2 = 31

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 31 + 9

Reorder the terms:
9 + 6x + x2 = 31 + 9

Combine like terms: 31 + 9 = 40
9 + 6x + x2 = 40

Factor a perfect square on the left side:
(x + 3)(x + 3) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + 3) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + 3 = 6.32455532

Simplifying
x + 3 = 6.32455532

Reorder the terms:
3 + x = 6.32455532

Solving
3 + x = 6.32455532

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 6.32455532 + -3

Combine like terms: 3 + -3 = 0
0 + x = 6.32455532 + -3
x = 6.32455532 + -3

Combine like terms: 6.32455532 + -3 = 3.32455532
x = 3.32455532

Simplifying
x = 3.32455532


Subproblem 2
x + 3 = -6.32455532

Simplifying
x + 3 = -6.32455532

Reorder the terms:
3 + x = -6.32455532

Solving
3 + x = -6.32455532

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -6.32455532 + -3

Combine like terms: 3 + -3 = 0
0 + x = -6.32455532 + -3
x = -6.32455532 + -3

Combine like terms: -6.32455532 + -3 = -9.32455532
x = -9.32455532

Simplifying
x = -9.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.32455532, -9.32455532}

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