m^2+10m+14m=-7

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Solution for m^2+10m+14m=-7 equation: 


Simplifying
m2 + 10m + 14m = -7

Reorder the terms:
10m + 14m + m2 = -7

Combine like terms: 10m + 14m = 24m
24m + m2 = -7

Solving
24m + m2 = -7

Solving for variable 'm'.

Reorder the terms:
7 + 24m + m2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 24m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 24m + -7 + m2 = 0 + -7

Reorder the terms:
7 + -7 + 24m + m2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 24m + m2 = 0 + -7
24m + m2 = 0 + -7

Combine like terms: 0 + -7 = -7
24m + m2 = -7

The m term is 24m.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24m + 144 + m2 = -7 + 144

Reorder the terms:
144 + 24m + m2 = -7 + 144

Combine like terms: -7 + 144 = 137
144 + 24m + m2 = 137

Factor a perfect square on the left side:
(m + 12)(m + 12) = 137

Calculate the square root of the right side: 11.704699911

Break this problem into two subproblems by setting 
(m + 12) equal to 11.704699911 and -11.704699911.


Subproblem 1
m + 12 = 11.704699911

Simplifying
m + 12 = 11.704699911

Reorder the terms:
12 + m = 11.704699911

Solving
12 + m = 11.704699911

Solving for variable 'm'.

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

Add '-12' to each side of the equation.
12 + -12 + m = 11.704699911 + -12

Combine like terms: 12 + -12 = 0
0 + m = 11.704699911 + -12
m = 11.704699911 + -12

Combine like terms: 11.704699911 + -12 = -0.295300089
m = -0.295300089

Simplifying
m = -0.295300089


Subproblem 2
m + 12 = -11.704699911

Simplifying
m + 12 = -11.704699911

Reorder the terms:
12 + m = -11.704699911

Solving
12 + m = -11.704699911

Solving for variable 'm'.

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

Add '-12' to each side of the equation.
12 + -12 + m = -11.704699911 + -12

Combine like terms: 12 + -12 = 0
0 + m = -11.704699911 + -12
m = -11.704699911 + -12

Combine like terms: -11.704699911 + -12 = -23.704699911
m = -23.704699911

Simplifying
m = -23.704699911


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.295300089, -23.704699911}

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