m^2+20m+100=7

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Solution for m^2+20m+100=7 equation: 


Simplifying
m2 + 20m + 100 = 7

Reorder the terms:
100 + 20m + m2 = 7

Solving
100 + 20m + m2 = 7

Solving for variable 'm'.

Reorder the terms:
100 + -7 + 20m + m2 = 7 + -7

Combine like terms: 100 + -7 = 93
93 + 20m + m2 = 7 + -7

Combine like terms: 7 + -7 = 0
93 + 20m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-93' to each side of the equation.
93 + 20m + -93 + m2 = 0 + -93

Reorder the terms:
93 + -93 + 20m + m2 = 0 + -93

Combine like terms: 93 + -93 = 0
0 + 20m + m2 = 0 + -93
20m + m2 = 0 + -93

Combine like terms: 0 + -93 = -93
20m + m2 = -93

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 = -93 + 100

Reorder the terms:
100 + 20m + m2 = -93 + 100

Combine like terms: -93 + 100 = 7
100 + 20m + m2 = 7

Factor a perfect square on the left side:
(m + 10)(m + 10) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(m + 10) equal to 2.645751311 and -2.645751311.


Subproblem 1
m + 10 = 2.645751311

Simplifying
m + 10 = 2.645751311

Reorder the terms:
10 + m = 2.645751311

Solving
10 + m = 2.645751311

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 = 2.645751311 + -10

Combine like terms: 10 + -10 = 0
0 + m = 2.645751311 + -10
m = 2.645751311 + -10

Combine like terms: 2.645751311 + -10 = -7.354248689
m = -7.354248689

Simplifying
m = -7.354248689


Subproblem 2
m + 10 = -2.645751311

Simplifying
m + 10 = -2.645751311

Reorder the terms:
10 + m = -2.645751311

Solving
10 + m = -2.645751311

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 = -2.645751311 + -10

Combine like terms: 10 + -10 = 0
0 + m = -2.645751311 + -10
m = -2.645751311 + -10

Combine like terms: -2.645751311 + -10 = -12.645751311
m = -12.645751311

Simplifying
m = -12.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-7.354248689, -12.645751311}

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