(m+10)(m+10)=15

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Solution for (m+10)(m+10)=15 equation: 


Simplifying
(m + 10)(m + 10) = 15

Reorder the terms:
(10 + m)(m + 10) = 15

Reorder the terms:
(10 + m)(10 + m) = 15

Multiply (10 + m) * (10 + m)
(10(10 + m) + m(10 + m)) = 15
((10 * 10 + m * 10) + m(10 + m)) = 15
((100 + 10m) + m(10 + m)) = 15
(100 + 10m + (10 * m + m * m)) = 15
(100 + 10m + (10m + m2)) = 15

Combine like terms: 10m + 10m = 20m
(100 + 20m + m2) = 15

Solving
100 + 20m + m2 = 15

Solving for variable 'm'.

Reorder the terms:
100 + -15 + 20m + m2 = 15 + -15

Combine like terms: 100 + -15 = 85
85 + 20m + m2 = 15 + -15

Combine like terms: 15 + -15 = 0
85 + 20m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-85' to each side of the equation.
85 + 20m + -85 + m2 = 0 + -85

Reorder the terms:
85 + -85 + 20m + m2 = 0 + -85

Combine like terms: 85 + -85 = 0
0 + 20m + m2 = 0 + -85
20m + m2 = 0 + -85

Combine like terms: 0 + -85 = -85
20m + m2 = -85

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 = -85 + 100

Reorder the terms:
100 + 20m + m2 = -85 + 100

Combine like terms: -85 + 100 = 15
100 + 20m + m2 = 15

Factor a perfect square on the left side:
(m + 10)(m + 10) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(m + 10) equal to 3.872983346 and -3.872983346.


Subproblem 1
m + 10 = 3.872983346

Simplifying
m + 10 = 3.872983346

Reorder the terms:
10 + m = 3.872983346

Solving
10 + m = 3.872983346

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 = 3.872983346 + -10

Combine like terms: 10 + -10 = 0
0 + m = 3.872983346 + -10
m = 3.872983346 + -10

Combine like terms: 3.872983346 + -10 = -6.127016654
m = -6.127016654

Simplifying
m = -6.127016654


Subproblem 2
m + 10 = -3.872983346

Simplifying
m + 10 = -3.872983346

Reorder the terms:
10 + m = -3.872983346

Solving
10 + m = -3.872983346

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 = -3.872983346 + -10

Combine like terms: 10 + -10 = 0
0 + m = -3.872983346 + -10
m = -3.872983346 + -10

Combine like terms: -3.872983346 + -10 = -13.872983346
m = -13.872983346

Simplifying
m = -13.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-6.127016654, -13.872983346}

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