30=(m^2+7m)+(m^2+7m)

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Solution for 30=(m^2+7m)+(m^2+7m) equation: 


Simplifying
30 = (m2 + 7m) + (m2 + 7m)

Reorder the terms:
30 = (7m + m2) + (m2 + 7m)

Remove parenthesis around (7m + m2)
30 = 7m + m2 + (m2 + 7m)

Reorder the terms:
30 = 7m + m2 + (7m + m2)

Remove parenthesis around (7m + m2)
30 = 7m + m2 + 7m + m2

Reorder the terms:
30 = 7m + 7m + m2 + m2

Combine like terms: 7m + 7m = 14m
30 = 14m + m2 + m2

Combine like terms: m2 + m2 = 2m2
30 = 14m + 2m2

Solving
30 = 14m + 2m2

Solving for variable 'm'.

Reorder the terms:
30 + -14m + -2m2 = 14m + -14m + 2m2 + -2m2

Combine like terms: 14m + -14m = 0
30 + -14m + -2m2 = 0 + 2m2 + -2m2
30 + -14m + -2m2 = 2m2 + -2m2

Combine like terms: 2m2 + -2m2 = 0
30 + -14m + -2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -7m + -1m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + -7m + -1m2)' equal to zero and attempt to solve:

Simplifying
15 + -7m + -1m2 = 0

Solving
15 + -7m + -1m2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-15 + 7m + m2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 7m + 15 + m2 = 0 + 15

Reorder the terms:
-15 + 15 + 7m + m2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 7m + m2 = 0 + 15
7m + m2 = 0 + 15

Combine like terms: 0 + 15 = 15
7m + m2 = 15

The m term is 7m.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7m + 12.25 + m2 = 15 + 12.25

Reorder the terms:
12.25 + 7m + m2 = 15 + 12.25

Combine like terms: 15 + 12.25 = 27.25
12.25 + 7m + m2 = 27.25

Factor a perfect square on the left side:
(m + 3.5)(m + 3.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(m + 3.5) equal to 5.220153254 and -5.220153254.


Subproblem 1
m + 3.5 = 5.220153254

Simplifying
m + 3.5 = 5.220153254

Reorder the terms:
3.5 + m = 5.220153254

Solving
3.5 + m = 5.220153254

Solving for variable 'm'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + m = 5.220153254 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + m = 5.220153254 + -3.5
m = 5.220153254 + -3.5

Combine like terms: 5.220153254 + -3.5 = 1.720153254
m = 1.720153254

Simplifying
m = 1.720153254


Subproblem 2
m + 3.5 = -5.220153254

Simplifying
m + 3.5 = -5.220153254

Reorder the terms:
3.5 + m = -5.220153254

Solving
3.5 + m = -5.220153254

Solving for variable 'm'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + m = -5.220153254 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + m = -5.220153254 + -3.5
m = -5.220153254 + -3.5

Combine like terms: -5.220153254 + -3.5 = -8.720153254
m = -8.720153254

Simplifying
m = -8.720153254


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.720153254, -8.720153254}
Solution
m = {1.720153254, -8.720153254}

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