6m+2(m+17)m=14

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Solution for 6m+2(m+17)m=14 equation: 


Simplifying
6m + 2(m + 17) * m = 14

Reorder the terms:
6m + 2(17 + m) * m = 14

Reorder the terms for easier multiplication:
6m + 2m(17 + m) = 14
6m + (17 * 2m + m * 2m) = 14
6m + (34m + 2m2) = 14

Combine like terms: 6m + 34m = 40m
40m + 2m2 = 14

Solving
40m + 2m2 = 14

Solving for variable 'm'.

Reorder the terms:
-14 + 40m + 2m2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 40m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 20m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 20m + m2)' equal to zero and attempt to solve:

Simplifying
-7 + 20m + m2 = 0

Solving
-7 + 20m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 20m + 7 + m2 = 0 + 7

Reorder the terms:
-7 + 7 + 20m + m2 = 0 + 7

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

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

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 = 7 + 100

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

Combine like terms: 7 + 100 = 107
100 + 20m + m2 = 107

Factor a perfect square on the left side:
(m + 10)(m + 10) = 107

Calculate the square root of the right side: 10.344080433

Break this problem into two subproblems by setting 
(m + 10) equal to 10.344080433 and -10.344080433.


Subproblem 1
m + 10 = 10.344080433

Simplifying
m + 10 = 10.344080433

Reorder the terms:
10 + m = 10.344080433

Solving
10 + m = 10.344080433

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 = 10.344080433 + -10

Combine like terms: 10 + -10 = 0
0 + m = 10.344080433 + -10
m = 10.344080433 + -10

Combine like terms: 10.344080433 + -10 = 0.344080433
m = 0.344080433

Simplifying
m = 0.344080433


Subproblem 2
m + 10 = -10.344080433

Simplifying
m + 10 = -10.344080433

Reorder the terms:
10 + m = -10.344080433

Solving
10 + m = -10.344080433

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 = -10.344080433 + -10

Combine like terms: 10 + -10 = 0
0 + m = -10.344080433 + -10
m = -10.344080433 + -10

Combine like terms: -10.344080433 + -10 = -20.344080433
m = -20.344080433

Simplifying
m = -20.344080433


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.344080433, -20.344080433}
Solution
m = {0.344080433, -20.344080433}

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