8(m)(m)-4m-2=0

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Solution for 8(m)(m)-4m-2=0 equation: 


Simplifying
8(m)(m) + -4m + -2 = 0

Multiply m * m
8m2 + -4m + -2 = 0

Reorder the terms:
-2 + -4m + 8m2 = 0

Solving
-2 + -4m + 8m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -2m + 4m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -2m + 4m2)' equal to zero and attempt to solve:

Simplifying
-1 + -2m + 4m2 = 0

Solving
-1 + -2m + 4m2 = 0

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

Divide each side by '4'.
-0.25 + -0.5m + m2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -0.5m + 0.25 + m2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -0.5m + m2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -0.5m + m2 = 0 + 0.25
-0.5m + m2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-0.5m + m2 = 0.25

The m term is -0.5m.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5m + 0.0625 + m2 = 0.25 + 0.0625

Reorder the terms:
0.0625 + -0.5m + m2 = 0.25 + 0.0625

Combine like terms: 0.25 + 0.0625 = 0.3125
0.0625 + -0.5m + m2 = 0.3125

Factor a perfect square on the left side:
(m + -0.25)(m + -0.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(m + -0.25) equal to 0.559016994 and -0.559016994.


Subproblem 1
m + -0.25 = 0.559016994

Simplifying
m + -0.25 = 0.559016994

Reorder the terms:
-0.25 + m = 0.559016994

Solving
-0.25 + m = 0.559016994

Solving for variable 'm'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + m = 0.559016994 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + m = 0.559016994 + 0.25
m = 0.559016994 + 0.25

Combine like terms: 0.559016994 + 0.25 = 0.809016994
m = 0.809016994

Simplifying
m = 0.809016994


Subproblem 2
m + -0.25 = -0.559016994

Simplifying
m + -0.25 = -0.559016994

Reorder the terms:
-0.25 + m = -0.559016994

Solving
-0.25 + m = -0.559016994

Solving for variable 'm'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + m = -0.559016994 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + m = -0.559016994 + 0.25
m = -0.559016994 + 0.25

Combine like terms: -0.559016994 + 0.25 = -0.309016994
m = -0.309016994

Simplifying
m = -0.309016994


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.809016994, -0.309016994}
Solution
m = {0.809016994, -0.309016994}

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