x^2+17x+31=0

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Solution for x^2+17x+31=0 equation: 


Simplifying
x2 + 17x + 31 = 0

Reorder the terms:
31 + 17x + x2 = 0

Solving
31 + 17x + 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 + 17x + -31 + x2 = 0 + -31

Reorder the terms:
31 + -31 + 17x + x2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + 17x + x2 = 0 + -31
17x + x2 = 0 + -31

Combine like terms: 0 + -31 = -31
17x + x2 = -31

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = -31 + 72.25

Reorder the terms:
72.25 + 17x + x2 = -31 + 72.25

Combine like terms: -31 + 72.25 = 41.25
72.25 + 17x + x2 = 41.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(x + 8.5) equal to 6.422616289 and -6.422616289.


Subproblem 1
x + 8.5 = 6.422616289

Simplifying
x + 8.5 = 6.422616289

Reorder the terms:
8.5 + x = 6.422616289

Solving
8.5 + x = 6.422616289

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 6.422616289 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 6.422616289 + -8.5
x = 6.422616289 + -8.5

Combine like terms: 6.422616289 + -8.5 = -2.077383711
x = -2.077383711

Simplifying
x = -2.077383711


Subproblem 2
x + 8.5 = -6.422616289

Simplifying
x + 8.5 = -6.422616289

Reorder the terms:
8.5 + x = -6.422616289

Solving
8.5 + x = -6.422616289

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = -6.422616289 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -6.422616289 + -8.5
x = -6.422616289 + -8.5

Combine like terms: -6.422616289 + -8.5 = -14.922616289
x = -14.922616289

Simplifying
x = -14.922616289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.077383711, -14.922616289}

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