8a^2-6a-1=0

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Solution for 8a^2-6a-1=0 equation: 


Simplifying
8a2 + -6a + -1 = 0

Reorder the terms:
-1 + -6a + 8a2 = 0

Solving
-1 + -6a + 8a2 = 0

Solving for variable 'a'.

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

Divide each side by '8'.
-0.125 + -0.75a + a2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -0.75a + 0.125 + a2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -0.75a + a2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -0.75a + a2 = 0 + 0.125
-0.75a + a2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-0.75a + a2 = 0.125

The a term is -0.75a.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75a + 0.140625 + a2 = 0.125 + 0.140625

Reorder the terms:
0.140625 + -0.75a + a2 = 0.125 + 0.140625

Combine like terms: 0.125 + 0.140625 = 0.265625
0.140625 + -0.75a + a2 = 0.265625

Factor a perfect square on the left side:
(a + -0.375)(a + -0.375) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(a + -0.375) equal to 0.515388203 and -0.515388203.


Subproblem 1
a + -0.375 = 0.515388203

Simplifying
a + -0.375 = 0.515388203

Reorder the terms:
-0.375 + a = 0.515388203

Solving
-0.375 + a = 0.515388203

Solving for variable 'a'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + a = 0.515388203 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + a = 0.515388203 + 0.375
a = 0.515388203 + 0.375

Combine like terms: 0.515388203 + 0.375 = 0.890388203
a = 0.890388203

Simplifying
a = 0.890388203


Subproblem 2
a + -0.375 = -0.515388203

Simplifying
a + -0.375 = -0.515388203

Reorder the terms:
-0.375 + a = -0.515388203

Solving
-0.375 + a = -0.515388203

Solving for variable 'a'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + a = -0.515388203 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + a = -0.515388203 + 0.375
a = -0.515388203 + 0.375

Combine like terms: -0.515388203 + 0.375 = -0.140388203
a = -0.140388203

Simplifying
a = -0.140388203


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.890388203, -0.140388203}

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