(9m-14)4=2m^2

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Solution for (9m-14)4=2m^2 equation: 


Simplifying
(9m + -14) * 4 = 2m2

Reorder the terms:
(-14 + 9m) * 4 = 2m2

Reorder the terms for easier multiplication:
4(-14 + 9m) = 2m2
(-14 * 4 + 9m * 4) = 2m2
(-56 + 36m) = 2m2

Solving
-56 + 36m = 2m2

Solving for variable 'm'.

Combine like terms: 2m2 + -2m2 = 0
-56 + 36m + -2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 18m + -1m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-28 + 18m + -1m2)' equal to zero and attempt to solve:

Simplifying
-28 + 18m + -1m2 = 0

Solving
-28 + 18m + -1m2 = 0

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

Divide each side by '-1'.
28 + -18m + m2 = 0

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -18m + -28 + m2 = 0 + -28

Reorder the terms:
28 + -28 + -18m + m2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -18m + m2 = 0 + -28
-18m + m2 = 0 + -28

Combine like terms: 0 + -28 = -28
-18m + m2 = -28

The m term is -18m.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18m + 81 + m2 = -28 + 81

Reorder the terms:
81 + -18m + m2 = -28 + 81

Combine like terms: -28 + 81 = 53
81 + -18m + m2 = 53

Factor a perfect square on the left side:
(m + -9)(m + -9) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(m + -9) equal to 7.280109889 and -7.280109889.


Subproblem 1
m + -9 = 7.280109889

Simplifying
m + -9 = 7.280109889

Reorder the terms:
-9 + m = 7.280109889

Solving
-9 + m = 7.280109889

Solving for variable 'm'.

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

Add '9' to each side of the equation.
-9 + 9 + m = 7.280109889 + 9

Combine like terms: -9 + 9 = 0
0 + m = 7.280109889 + 9
m = 7.280109889 + 9

Combine like terms: 7.280109889 + 9 = 16.280109889
m = 16.280109889

Simplifying
m = 16.280109889


Subproblem 2
m + -9 = -7.280109889

Simplifying
m + -9 = -7.280109889

Reorder the terms:
-9 + m = -7.280109889

Solving
-9 + m = -7.280109889

Solving for variable 'm'.

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

Add '9' to each side of the equation.
-9 + 9 + m = -7.280109889 + 9

Combine like terms: -9 + 9 = 0
0 + m = -7.280109889 + 9
m = -7.280109889 + 9

Combine like terms: -7.280109889 + 9 = 1.719890111
m = 1.719890111

Simplifying
m = 1.719890111


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {16.280109889, 1.719890111}
Solution
m = {16.280109889, 1.719890111}

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