4m^2+16m-8=0

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Solution for 4m^2+16m-8=0 equation: 


Simplifying
4m2 + 16m + -8 = 0

Reorder the terms:
-8 + 16m + 4m2 = 0

Solving
-8 + 16m + 4m2 = 0

Solving for variable 'm'.

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

Ignore the factor 4.

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

Simplifying
-2 + 4m + m2 = 0

Solving
-2 + 4m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4m + 2 + m2 = 0 + 2

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

Combine like terms: -2 + 2 = 0
0 + 4m + m2 = 0 + 2
4m + m2 = 0 + 2

Combine like terms: 0 + 2 = 2
4m + m2 = 2

The m term is 4m.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4m + 4 + m2 = 2 + 4

Reorder the terms:
4 + 4m + m2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + 4m + m2 = 6

Factor a perfect square on the left side:
(m + 2)(m + 2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(m + 2) equal to 2.449489743 and -2.449489743.


Subproblem 1
m + 2 = 2.449489743

Simplifying
m + 2 = 2.449489743

Reorder the terms:
2 + m = 2.449489743

Solving
2 + m = 2.449489743

Solving for variable 'm'.

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

Add '-2' to each side of the equation.
2 + -2 + m = 2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + m = 2.449489743 + -2
m = 2.449489743 + -2

Combine like terms: 2.449489743 + -2 = 0.449489743
m = 0.449489743

Simplifying
m = 0.449489743


Subproblem 2
m + 2 = -2.449489743

Simplifying
m + 2 = -2.449489743

Reorder the terms:
2 + m = -2.449489743

Solving
2 + m = -2.449489743

Solving for variable 'm'.

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

Add '-2' to each side of the equation.
2 + -2 + m = -2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + m = -2.449489743 + -2
m = -2.449489743 + -2

Combine like terms: -2.449489743 + -2 = -4.449489743
m = -4.449489743

Simplifying
m = -4.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.449489743, -4.449489743}
Solution
m = {0.449489743, -4.449489743}

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