4m^2-18m-14=0

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Solution for 4m^2-18m-14=0 equation: 


Simplifying
4m2 + -18m + -14 = 0

Reorder the terms:
-14 + -18m + 4m2 = 0

Solving
-14 + -18m + 4m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -9m + 2m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -9m + 2m2)' equal to zero and attempt to solve:

Simplifying
-7 + -9m + 2m2 = 0

Solving
-7 + -9m + 2m2 = 0

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

Divide each side by '2'.
-3.5 + -4.5m + m2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -4.5m + 3.5 + m2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -4.5m + m2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -4.5m + m2 = 0 + 3.5
-4.5m + m2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-4.5m + m2 = 3.5

The m term is -4.5m.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5m + 5.0625 + m2 = 3.5 + 5.0625

Reorder the terms:
5.0625 + -4.5m + m2 = 3.5 + 5.0625

Combine like terms: 3.5 + 5.0625 = 8.5625
5.0625 + -4.5m + m2 = 8.5625

Factor a perfect square on the left side:
(m + -2.25)(m + -2.25) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(m + -2.25) equal to 2.926174978 and -2.926174978.


Subproblem 1
m + -2.25 = 2.926174978

Simplifying
m + -2.25 = 2.926174978

Reorder the terms:
-2.25 + m = 2.926174978

Solving
-2.25 + m = 2.926174978

Solving for variable 'm'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + m = 2.926174978 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + m = 2.926174978 + 2.25
m = 2.926174978 + 2.25

Combine like terms: 2.926174978 + 2.25 = 5.176174978
m = 5.176174978

Simplifying
m = 5.176174978


Subproblem 2
m + -2.25 = -2.926174978

Simplifying
m + -2.25 = -2.926174978

Reorder the terms:
-2.25 + m = -2.926174978

Solving
-2.25 + m = -2.926174978

Solving for variable 'm'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + m = -2.926174978 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + m = -2.926174978 + 2.25
m = -2.926174978 + 2.25

Combine like terms: -2.926174978 + 2.25 = -0.676174978
m = -0.676174978

Simplifying
m = -0.676174978


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.176174978, -0.676174978}
Solution
m = {5.176174978, -0.676174978}

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