8m^2-10m-1=0

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Solution for 8m^2-10m-1=0 equation: 


Simplifying
8m2 + -10m + -1 = 0

Reorder the terms:
-1 + -10m + 8m2 = 0

Solving
-1 + -10m + 8m2 = 0

Solving for variable 'm'.

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

Divide each side by '8'.
-0.125 + -1.25m + m2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -1.25m + 0.125 + m2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -1.25m + m2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -1.25m + m2 = 0 + 0.125
-1.25m + m2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-1.25m + m2 = 0.125

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 = 0.125 + 0.390625

Reorder the terms:
0.390625 + -1.25m + m2 = 0.125 + 0.390625

Combine like terms: 0.125 + 0.390625 = 0.515625
0.390625 + -1.25m + m2 = 0.515625

Factor a perfect square on the left side:
(m + -0.625)(m + -0.625) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(m + -0.625) equal to 0.718070331 and -0.718070331.


Subproblem 1
m + -0.625 = 0.718070331

Simplifying
m + -0.625 = 0.718070331

Reorder the terms:
-0.625 + m = 0.718070331

Solving
-0.625 + m = 0.718070331

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 = 0.718070331 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + m = 0.718070331 + 0.625
m = 0.718070331 + 0.625

Combine like terms: 0.718070331 + 0.625 = 1.343070331
m = 1.343070331

Simplifying
m = 1.343070331


Subproblem 2
m + -0.625 = -0.718070331

Simplifying
m + -0.625 = -0.718070331

Reorder the terms:
-0.625 + m = -0.718070331

Solving
-0.625 + m = -0.718070331

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 = -0.718070331 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + m = -0.718070331 + 0.625
m = -0.718070331 + 0.625

Combine like terms: -0.718070331 + 0.625 = -0.093070331
m = -0.093070331

Simplifying
m = -0.093070331


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.343070331, -0.093070331}

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