m^2+20m+78=0

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Solution for m^2+20m+78=0 equation: 


Simplifying
m2 + 20m + 78 = 0

Reorder the terms:
78 + 20m + m2 = 0

Solving
78 + 20m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-78' to each side of the equation.
78 + 20m + -78 + m2 = 0 + -78

Reorder the terms:
78 + -78 + 20m + m2 = 0 + -78

Combine like terms: 78 + -78 = 0
0 + 20m + m2 = 0 + -78
20m + m2 = 0 + -78

Combine like terms: 0 + -78 = -78
20m + m2 = -78

The m term is 20m.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20m + 100 + m2 = -78 + 100

Reorder the terms:
100 + 20m + m2 = -78 + 100

Combine like terms: -78 + 100 = 22
100 + 20m + m2 = 22

Factor a perfect square on the left side:
(m + 10)(m + 10) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(m + 10) equal to 4.69041576 and -4.69041576.


Subproblem 1
m + 10 = 4.69041576

Simplifying
m + 10 = 4.69041576

Reorder the terms:
10 + m = 4.69041576

Solving
10 + m = 4.69041576

Solving for variable 'm'.

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

Add '-10' to each side of the equation.
10 + -10 + m = 4.69041576 + -10

Combine like terms: 10 + -10 = 0
0 + m = 4.69041576 + -10
m = 4.69041576 + -10

Combine like terms: 4.69041576 + -10 = -5.30958424
m = -5.30958424

Simplifying
m = -5.30958424


Subproblem 2
m + 10 = -4.69041576

Simplifying
m + 10 = -4.69041576

Reorder the terms:
10 + m = -4.69041576

Solving
10 + m = -4.69041576

Solving for variable 'm'.

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

Add '-10' to each side of the equation.
10 + -10 + m = -4.69041576 + -10

Combine like terms: 10 + -10 = 0
0 + m = -4.69041576 + -10
m = -4.69041576 + -10

Combine like terms: -4.69041576 + -10 = -14.69041576
m = -14.69041576

Simplifying
m = -14.69041576


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-5.30958424, -14.69041576}

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