(9m)(25m+22)=90

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Solution for (9m)(25m+22)=90 equation: 


Simplifying
(9m)(25m + 22) = 90

Remove parenthesis around (9m)
9m(25m + 22) = 90

Reorder the terms:
9m(22 + 25m) = 90
(22 * 9m + 25m * 9m) = 90
(198m + 225m2) = 90

Solving
198m + 225m2 = 90

Solving for variable 'm'.

Reorder the terms:
-90 + 198m + 225m2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 198m + 225m2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-10 + 22m + 25m2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-10 + 22m + 25m2)' equal to zero and attempt to solve:

Simplifying
-10 + 22m + 25m2 = 0

Solving
-10 + 22m + 25m2 = 0

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

Divide each side by '25'.
-0.4 + 0.88m + m2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.88m + 0.4 + m2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.88m + m2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.88m + m2 = 0 + 0.4
0.88m + m2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.88m + m2 = 0.4

The m term is 0.88m.  Take half its coefficient (0.44).
Square it (0.1936) and add it to both sides.

Add '0.1936' to each side of the equation.
0.88m + 0.1936 + m2 = 0.4 + 0.1936

Reorder the terms:
0.1936 + 0.88m + m2 = 0.4 + 0.1936

Combine like terms: 0.4 + 0.1936 = 0.5936
0.1936 + 0.88m + m2 = 0.5936

Factor a perfect square on the left side:
(m + 0.44)(m + 0.44) = 0.5936

Calculate the square root of the right side: 0.770454411

Break this problem into two subproblems by setting 
(m + 0.44) equal to 0.770454411 and -0.770454411.


Subproblem 1
m + 0.44 = 0.770454411

Simplifying
m + 0.44 = 0.770454411

Reorder the terms:
0.44 + m = 0.770454411

Solving
0.44 + m = 0.770454411

Solving for variable 'm'.

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

Add '-0.44' to each side of the equation.
0.44 + -0.44 + m = 0.770454411 + -0.44

Combine like terms: 0.44 + -0.44 = 0.00
0.00 + m = 0.770454411 + -0.44
m = 0.770454411 + -0.44

Combine like terms: 0.770454411 + -0.44 = 0.330454411
m = 0.330454411

Simplifying
m = 0.330454411


Subproblem 2
m + 0.44 = -0.770454411

Simplifying
m + 0.44 = -0.770454411

Reorder the terms:
0.44 + m = -0.770454411

Solving
0.44 + m = -0.770454411

Solving for variable 'm'.

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

Add '-0.44' to each side of the equation.
0.44 + -0.44 + m = -0.770454411 + -0.44

Combine like terms: 0.44 + -0.44 = 0.00
0.00 + m = -0.770454411 + -0.44
m = -0.770454411 + -0.44

Combine like terms: -0.770454411 + -0.44 = -1.210454411
m = -1.210454411

Simplifying
m = -1.210454411


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.330454411, -1.210454411}
Solution
m = {0.330454411, -1.210454411}

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