8m(4m+1)=170

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Solution for 8m(4m+1)=170 equation: 


Simplifying
8m(4m + 1) = 170

Reorder the terms:
8m(1 + 4m) = 170
(1 * 8m + 4m * 8m) = 170
(8m + 32m2) = 170

Solving
8m + 32m2 = 170

Solving for variable 'm'.

Reorder the terms:
-170 + 8m + 32m2 = 170 + -170

Combine like terms: 170 + -170 = 0
-170 + 8m + 32m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-85 + 4m + 16m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-85 + 4m + 16m2)' equal to zero and attempt to solve:

Simplifying
-85 + 4m + 16m2 = 0

Solving
-85 + 4m + 16m2 = 0

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

Divide each side by '16'.
-5.3125 + 0.25m + m2 = 0

Move the constant term to the right:

Add '5.3125' to each side of the equation.
-5.3125 + 0.25m + 5.3125 + m2 = 0 + 5.3125

Reorder the terms:
-5.3125 + 5.3125 + 0.25m + m2 = 0 + 5.3125

Combine like terms: -5.3125 + 5.3125 = 0.0000
0.0000 + 0.25m + m2 = 0 + 5.3125
0.25m + m2 = 0 + 5.3125

Combine like terms: 0 + 5.3125 = 5.3125
0.25m + m2 = 5.3125

The m term is 0.25m.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25m + 0.015625 + m2 = 5.3125 + 0.015625

Reorder the terms:
0.015625 + 0.25m + m2 = 5.3125 + 0.015625

Combine like terms: 5.3125 + 0.015625 = 5.328125
0.015625 + 0.25m + m2 = 5.328125

Factor a perfect square on the left side:
(m + 0.125)(m + 0.125) = 5.328125

Calculate the square root of the right side: 2.308273164

Break this problem into two subproblems by setting 
(m + 0.125) equal to 2.308273164 and -2.308273164.


Subproblem 1
m + 0.125 = 2.308273164

Simplifying
m + 0.125 = 2.308273164

Reorder the terms:
0.125 + m = 2.308273164

Solving
0.125 + m = 2.308273164

Solving for variable 'm'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + m = 2.308273164 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + m = 2.308273164 + -0.125
m = 2.308273164 + -0.125

Combine like terms: 2.308273164 + -0.125 = 2.183273164
m = 2.183273164

Simplifying
m = 2.183273164


Subproblem 2
m + 0.125 = -2.308273164

Simplifying
m + 0.125 = -2.308273164

Reorder the terms:
0.125 + m = -2.308273164

Solving
0.125 + m = -2.308273164

Solving for variable 'm'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + m = -2.308273164 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + m = -2.308273164 + -0.125
m = -2.308273164 + -0.125

Combine like terms: -2.308273164 + -0.125 = -2.433273164
m = -2.433273164

Simplifying
m = -2.433273164


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.183273164, -2.433273164}
Solution
m = {2.183273164, -2.433273164}

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