8x^2-2x-5=0

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Solution for 8x^2-2x-5=0 equation: 


Simplifying
8x2 + -2x + -5 = 0

Reorder the terms:
-5 + -2x + 8x2 = 0

Solving
-5 + -2x + 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'.
-0.625 + -0.25x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -0.25x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -0.25x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -0.25x + x2 = 0 + 0.625
-0.25x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-0.25x + x2 = 0.625

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 0.625 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 0.625 + 0.015625

Combine like terms: 0.625 + 0.015625 = 0.640625
0.015625 + -0.25x + x2 = 0.640625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(x + -0.125) equal to 0.80039053 and -0.80039053.


Subproblem 1
x + -0.125 = 0.80039053

Simplifying
x + -0.125 = 0.80039053

Reorder the terms:
-0.125 + x = 0.80039053

Solving
-0.125 + x = 0.80039053

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = 0.80039053 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 0.80039053 + 0.125
x = 0.80039053 + 0.125

Combine like terms: 0.80039053 + 0.125 = 0.92539053
x = 0.92539053

Simplifying
x = 0.92539053


Subproblem 2
x + -0.125 = -0.80039053

Simplifying
x + -0.125 = -0.80039053

Reorder the terms:
-0.125 + x = -0.80039053

Solving
-0.125 + x = -0.80039053

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = -0.80039053 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -0.80039053 + 0.125
x = -0.80039053 + 0.125

Combine like terms: -0.80039053 + 0.125 = -0.67539053
x = -0.67539053

Simplifying
x = -0.67539053


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.92539053, -0.67539053}

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