-8x^2+2x+9=0

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Solution for -8x^2+2x+9=0 equation: 


Simplifying
-8x2 + 2x + 9 = 0

Reorder the terms:
9 + 2x + -8x2 = 0

Solving
9 + 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'.
-1.125 + -0.25x + x2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -0.25x + 1.125 + x2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -0.25x + x2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -0.25x + x2 = 0 + 1.125
-0.25x + x2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-0.25x + x2 = 1.125

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 = 1.125 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 1.125 + 0.015625

Combine like terms: 1.125 + 0.015625 = 1.140625
0.015625 + -0.25x + x2 = 1.140625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.068000468 and -1.068000468.


Subproblem 1
x + -0.125 = 1.068000468

Simplifying
x + -0.125 = 1.068000468

Reorder the terms:
-0.125 + x = 1.068000468

Solving
-0.125 + x = 1.068000468

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 = 1.068000468 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 1.068000468 + 0.125
x = 1.068000468 + 0.125

Combine like terms: 1.068000468 + 0.125 = 1.193000468
x = 1.193000468

Simplifying
x = 1.193000468


Subproblem 2
x + -0.125 = -1.068000468

Simplifying
x + -0.125 = -1.068000468

Reorder the terms:
-0.125 + x = -1.068000468

Solving
-0.125 + x = -1.068000468

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 = -1.068000468 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -1.068000468 + 0.125
x = -1.068000468 + 0.125

Combine like terms: -1.068000468 + 0.125 = -0.943000468
x = -0.943000468

Simplifying
x = -0.943000468


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.193000468, -0.943000468}

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