8x^2-8x-1=0

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Solution for 8x^2-8x-1=0 equation:


Simplifying
8x2 + -8x + -1 = 0

Reorder the terms:
-1 + -8x + 8x2 = 0

Solving
-1 + -8x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-0.125 + -1x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -1x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -1x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -1x + x2 = 0 + 0.125
-1x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-1x + x2 = 0.125

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 0.125 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.125 + 0.25

Combine like terms: 0.125 + 0.25 = 0.375
0.25 + -1x + x2 = 0.375

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.375

Calculate the square root of the right side: 0.612372436

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.612372436 and -0.612372436.

Subproblem 1

x + -0.5 = 0.612372436 Simplifying x + -0.5 = 0.612372436 Reorder the terms: -0.5 + x = 0.612372436 Solving -0.5 + x = 0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.612372436 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.612372436 + 0.5 x = 0.612372436 + 0.5 Combine like terms: 0.612372436 + 0.5 = 1.112372436 x = 1.112372436 Simplifying x = 1.112372436

Subproblem 2

x + -0.5 = -0.612372436 Simplifying x + -0.5 = -0.612372436 Reorder the terms: -0.5 + x = -0.612372436 Solving -0.5 + x = -0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.612372436 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.612372436 + 0.5 x = -0.612372436 + 0.5 Combine like terms: -0.612372436 + 0.5 = -0.112372436 x = -0.112372436 Simplifying x = -0.112372436

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.112372436, -0.112372436}

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