2m(m+10)=180

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Solution for 2m(m+10)=180 equation: 


Simplifying
2m(m + 10) = 180

Reorder the terms:
2m(10 + m) = 180
(10 * 2m + m * 2m) = 180
(20m + 2m2) = 180

Solving
20m + 2m2 = 180

Solving for variable 'm'.

Reorder the terms:
-180 + 20m + 2m2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 20m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 10m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + 10m + m2)' equal to zero and attempt to solve:

Simplifying
-90 + 10m + m2 = 0

Solving
-90 + 10m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 10m + 90 + m2 = 0 + 90

Reorder the terms:
-90 + 90 + 10m + m2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 10m + m2 = 0 + 90
10m + m2 = 0 + 90

Combine like terms: 0 + 90 = 90
10m + m2 = 90

The m term is 10m.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10m + 25 + m2 = 90 + 25

Reorder the terms:
25 + 10m + m2 = 90 + 25

Combine like terms: 90 + 25 = 115
25 + 10m + m2 = 115

Factor a perfect square on the left side:
(m + 5)(m + 5) = 115

Calculate the square root of the right side: 10.723805295

Break this problem into two subproblems by setting 
(m + 5) equal to 10.723805295 and -10.723805295.


Subproblem 1
m + 5 = 10.723805295

Simplifying
m + 5 = 10.723805295

Reorder the terms:
5 + m = 10.723805295

Solving
5 + m = 10.723805295

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + -5 + m = 10.723805295 + -5

Combine like terms: 5 + -5 = 0
0 + m = 10.723805295 + -5
m = 10.723805295 + -5

Combine like terms: 10.723805295 + -5 = 5.723805295
m = 5.723805295

Simplifying
m = 5.723805295


Subproblem 2
m + 5 = -10.723805295

Simplifying
m + 5 = -10.723805295

Reorder the terms:
5 + m = -10.723805295

Solving
5 + m = -10.723805295

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + -5 + m = -10.723805295 + -5

Combine like terms: 5 + -5 = 0
0 + m = -10.723805295 + -5
m = -10.723805295 + -5

Combine like terms: -10.723805295 + -5 = -15.723805295
m = -15.723805295

Simplifying
m = -15.723805295


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.723805295, -15.723805295}
Solution
m = {5.723805295, -15.723805295}

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