m^2+14m+31=0

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Solution for m^2+14m+31=0 equation: 


Simplifying
m2 + 14m + 31 = 0

Reorder the terms:
31 + 14m + m2 = 0

Solving
31 + 14m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + 14m + -31 + m2 = 0 + -31

Reorder the terms:
31 + -31 + 14m + m2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + 14m + m2 = 0 + -31
14m + m2 = 0 + -31

Combine like terms: 0 + -31 = -31
14m + m2 = -31

The m term is 14m.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14m + 49 + m2 = -31 + 49

Reorder the terms:
49 + 14m + m2 = -31 + 49

Combine like terms: -31 + 49 = 18
49 + 14m + m2 = 18

Factor a perfect square on the left side:
(m + 7)(m + 7) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(m + 7) equal to 4.242640687 and -4.242640687.


Subproblem 1
m + 7 = 4.242640687

Simplifying
m + 7 = 4.242640687

Reorder the terms:
7 + m = 4.242640687

Solving
7 + m = 4.242640687

Solving for variable 'm'.

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

Add '-7' to each side of the equation.
7 + -7 + m = 4.242640687 + -7

Combine like terms: 7 + -7 = 0
0 + m = 4.242640687 + -7
m = 4.242640687 + -7

Combine like terms: 4.242640687 + -7 = -2.757359313
m = -2.757359313

Simplifying
m = -2.757359313


Subproblem 2
m + 7 = -4.242640687

Simplifying
m + 7 = -4.242640687

Reorder the terms:
7 + m = -4.242640687

Solving
7 + m = -4.242640687

Solving for variable 'm'.

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

Add '-7' to each side of the equation.
7 + -7 + m = -4.242640687 + -7

Combine like terms: 7 + -7 = 0
0 + m = -4.242640687 + -7
m = -4.242640687 + -7

Combine like terms: -4.242640687 + -7 = -11.242640687
m = -11.242640687

Simplifying
m = -11.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-2.757359313, -11.242640687}

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