8m^2-10m-20=0

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Solution for 8m^2-10m-20=0 equation: 


Simplifying
8m2 + -10m + -20 = 0

Reorder the terms:
-20 + -10m + 8m2 = 0

Solving
-20 + -10m + 8m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -5m + 4m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + -5m + 4m2)' equal to zero and attempt to solve:

Simplifying
-10 + -5m + 4m2 = 0

Solving
-10 + -5m + 4m2 = 0

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

Divide each side by '4'.
-2.5 + -1.25m + m2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -1.25m + 2.5 + m2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -1.25m + m2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -1.25m + m2 = 0 + 2.5
-1.25m + m2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-1.25m + m2 = 2.5

The m term is -1.25m.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25m + 0.390625 + m2 = 2.5 + 0.390625

Reorder the terms:
0.390625 + -1.25m + m2 = 2.5 + 0.390625

Combine like terms: 2.5 + 0.390625 = 2.890625
0.390625 + -1.25m + m2 = 2.890625

Factor a perfect square on the left side:
(m + -0.625)(m + -0.625) = 2.890625

Calculate the square root of the right side: 1.700183814

Break this problem into two subproblems by setting 
(m + -0.625) equal to 1.700183814 and -1.700183814.


Subproblem 1
m + -0.625 = 1.700183814

Simplifying
m + -0.625 = 1.700183814

Reorder the terms:
-0.625 + m = 1.700183814

Solving
-0.625 + m = 1.700183814

Solving for variable 'm'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + m = 1.700183814 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + m = 1.700183814 + 0.625
m = 1.700183814 + 0.625

Combine like terms: 1.700183814 + 0.625 = 2.325183814
m = 2.325183814

Simplifying
m = 2.325183814


Subproblem 2
m + -0.625 = -1.700183814

Simplifying
m + -0.625 = -1.700183814

Reorder the terms:
-0.625 + m = -1.700183814

Solving
-0.625 + m = -1.700183814

Solving for variable 'm'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + m = -1.700183814 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + m = -1.700183814 + 0.625
m = -1.700183814 + 0.625

Combine like terms: -1.700183814 + 0.625 = -1.075183814
m = -1.075183814

Simplifying
m = -1.075183814


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.325183814, -1.075183814}
Solution
m = {2.325183814, -1.075183814}

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