-2m(m+7)=-22

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Solution for -2m(m+7)=-22 equation: 


Simplifying
-2m(m + 7) = -22

Reorder the terms:
-2m(7 + m) = -22
(7 * -2m + m * -2m) = -22
(-14m + -2m2) = -22

Solving
-14m + -2m2 = -22

Solving for variable 'm'.

Reorder the terms:
22 + -14m + -2m2 = -22 + 22

Combine like terms: -22 + 22 = 0
22 + -14m + -2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -7m + -1m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(11 + -7m + -1m2)' equal to zero and attempt to solve:

Simplifying
11 + -7m + -1m2 = 0

Solving
11 + -7m + -1m2 = 0

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

Divide each side by '-1'.
-11 + 7m + m2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 7m + 11 + m2 = 0 + 11

Reorder the terms:
-11 + 11 + 7m + m2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 7m + m2 = 0 + 11
7m + m2 = 0 + 11

Combine like terms: 0 + 11 = 11
7m + m2 = 11

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 = 11 + 12.25

Reorder the terms:
12.25 + 7m + m2 = 11 + 12.25

Combine like terms: 11 + 12.25 = 23.25
12.25 + 7m + m2 = 23.25

Factor a perfect square on the left side:
(m + 3.5)(m + 3.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(m + 3.5) equal to 4.82182538 and -4.82182538.


Subproblem 1
m + 3.5 = 4.82182538

Simplifying
m + 3.5 = 4.82182538

Reorder the terms:
3.5 + m = 4.82182538

Solving
3.5 + m = 4.82182538

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 = 4.82182538 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + m = 4.82182538 + -3.5
m = 4.82182538 + -3.5

Combine like terms: 4.82182538 + -3.5 = 1.32182538
m = 1.32182538

Simplifying
m = 1.32182538


Subproblem 2
m + 3.5 = -4.82182538

Simplifying
m + 3.5 = -4.82182538

Reorder the terms:
3.5 + m = -4.82182538

Solving
3.5 + m = -4.82182538

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 = -4.82182538 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + m = -4.82182538 + -3.5
m = -4.82182538 + -3.5

Combine like terms: -4.82182538 + -3.5 = -8.32182538
m = -8.32182538

Simplifying
m = -8.32182538


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.32182538, -8.32182538}
Solution
m = {1.32182538, -8.32182538}

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