16m^2+160m+400=8

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Solution for 16m^2+160m+400=8 equation: 


Simplifying
16m2 + 160m + 400 = 8

Reorder the terms:
400 + 160m + 16m2 = 8

Solving
400 + 160m + 16m2 = 8

Solving for variable 'm'.

Reorder the terms:
400 + -8 + 160m + 16m2 = 8 + -8

Combine like terms: 400 + -8 = 392
392 + 160m + 16m2 = 8 + -8

Combine like terms: 8 + -8 = 0
392 + 160m + 16m2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(49 + 20m + 2m2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(49 + 20m + 2m2)' equal to zero and attempt to solve:

Simplifying
49 + 20m + 2m2 = 0

Solving
49 + 20m + 2m2 = 0

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

Divide each side by '2'.
24.5 + 10m + m2 = 0

Move the constant term to the right:

Add '-24.5' to each side of the equation.
24.5 + 10m + -24.5 + m2 = 0 + -24.5

Reorder the terms:
24.5 + -24.5 + 10m + m2 = 0 + -24.5

Combine like terms: 24.5 + -24.5 = 0.0
0.0 + 10m + m2 = 0 + -24.5
10m + m2 = 0 + -24.5

Combine like terms: 0 + -24.5 = -24.5
10m + m2 = -24.5

The m term is 10m.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10m + 25 + m2 = -24.5 + 25

Reorder the terms:
25 + 10m + m2 = -24.5 + 25

Combine like terms: -24.5 + 25 = 0.5
25 + 10m + m2 = 0.5

Factor a perfect square on the left side:
(m + 5)(m + 5) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(m + 5) equal to 0.707106781 and -0.707106781.


Subproblem 1
m + 5 = 0.707106781

Simplifying
m + 5 = 0.707106781

Reorder the terms:
5 + m = 0.707106781

Solving
5 + m = 0.707106781

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + -5 + m = 0.707106781 + -5

Combine like terms: 5 + -5 = 0
0 + m = 0.707106781 + -5
m = 0.707106781 + -5

Combine like terms: 0.707106781 + -5 = -4.292893219
m = -4.292893219

Simplifying
m = -4.292893219


Subproblem 2
m + 5 = -0.707106781

Simplifying
m + 5 = -0.707106781

Reorder the terms:
5 + m = -0.707106781

Solving
5 + m = -0.707106781

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + -5 + m = -0.707106781 + -5

Combine like terms: 5 + -5 = 0
0 + m = -0.707106781 + -5
m = -0.707106781 + -5

Combine like terms: -0.707106781 + -5 = -5.707106781
m = -5.707106781

Simplifying
m = -5.707106781


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-4.292893219, -5.707106781}
Solution
m = {-4.292893219, -5.707106781}

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