16m^2+2m-4=0

Solution for 16m^2+2m-4=0 equation:

Simplifying
16m2 + 2m + -4 = 0

Reorder the terms:
-4 + 2m + 16m2 = 0

Solving
-4 + 2m + 16m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + m + 8m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + m + 8m2)' equal to zero and attempt to solve:

Simplifying
-2 + m + 8m2 = 0

Solving
-2 + m + 8m2 = 0

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

Divide each side by '8'.
-0.25 + 0.125m + m2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.125m + 0.25 + m2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.125m + m2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.125m + m2 = 0 + 0.25
0.125m + m2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.125m + m2 = 0.25

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

Add '0.25' to each side of the equation.
0.125m + 0.25 + m2 = 0.25 + 0.25

Reorder the terms:
0.25 + 0.125m + m2 = 0.25 + 0.25

Combine like terms: 0.25 + 0.25 = 0.5
0.25 + 0.125m + m2 = 0.5

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(m + 0.5) equal to 0.707106781 and -0.707106781.

Subproblem 1
m + 0.5 = 0.707106781

Simplifying
m + 0.5 = 0.707106781

Reorder the terms:
0.5 + m = 0.707106781

Solving
0.5 + m = 0.707106781

Solving for variable 'm'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + m = 0.707106781 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = 0.707106781 + -0.5
m = 0.707106781 + -0.5

Combine like terms: 0.707106781 + -0.5 = 0.207106781
m = 0.207106781

Simplifying
m = 0.207106781

Subproblem 2
m + 0.5 = -0.707106781

Simplifying
m + 0.5 = -0.707106781

Reorder the terms:
0.5 + m = -0.707106781

Solving
0.5 + m = -0.707106781

Solving for variable 'm'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + m = -0.707106781 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = -0.707106781 + -0.5
m = -0.707106781 + -0.5

Combine like terms: -0.707106781 + -0.5 = -1.207106781
m = -1.207106781

Simplifying
m = -1.207106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.207106781, -1.207106781}
Solution
m = {0.207106781, -1.207106781}