8x^2-2x-17=0

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Solution for 8x^2-2x-17=0 equation: 


Simplifying
8x2 + -2x + -17 = 0

Reorder the terms:
-17 + -2x + 8x2 = 0

Solving
-17 + -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'.
-2.125 + -0.25x + x2 = 0

Move the constant term to the right:

Add '2.125' to each side of the equation.
-2.125 + -0.25x + 2.125 + x2 = 0 + 2.125

Reorder the terms:
-2.125 + 2.125 + -0.25x + x2 = 0 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + -0.25x + x2 = 0 + 2.125
-0.25x + x2 = 0 + 2.125

Combine like terms: 0 + 2.125 = 2.125
-0.25x + x2 = 2.125

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 = 2.125 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 2.125 + 0.015625

Combine like terms: 2.125 + 0.015625 = 2.140625
0.015625 + -0.25x + x2 = 2.140625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 2.140625

Calculate the square root of the right side: 1.463087489

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.463087489 and -1.463087489.


Subproblem 1
x + -0.125 = 1.463087489

Simplifying
x + -0.125 = 1.463087489

Reorder the terms:
-0.125 + x = 1.463087489

Solving
-0.125 + x = 1.463087489

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 = 1.463087489 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 1.463087489 + 0.125
x = 1.463087489 + 0.125

Combine like terms: 1.463087489 + 0.125 = 1.588087489
x = 1.588087489

Simplifying
x = 1.588087489


Subproblem 2
x + -0.125 = -1.463087489

Simplifying
x + -0.125 = -1.463087489

Reorder the terms:
-0.125 + x = -1.463087489

Solving
-0.125 + x = -1.463087489

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 = -1.463087489 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -1.463087489 + 0.125
x = -1.463087489 + 0.125

Combine like terms: -1.463087489 + 0.125 = -1.338087489
x = -1.338087489

Simplifying
x = -1.338087489


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.588087489, -1.338087489}

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