8x^2+9x-5=0

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Solution for 8x^2+9x-5=0 equation: 


Simplifying
8x2 + 9x + -5 = 0

Reorder the terms:
-5 + 9x + 8x2 = 0

Solving
-5 + 9x + 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 + 1.125x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + 1.125x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + 1.125x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + 1.125x + x2 = 0 + 0.625
1.125x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
1.125x + x2 = 0.625

The x term is 1.125x.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125x + 0.31640625 + x2 = 0.625 + 0.31640625

Reorder the terms:
0.31640625 + 1.125x + x2 = 0.625 + 0.31640625

Combine like terms: 0.625 + 0.31640625 = 0.94140625
0.31640625 + 1.125x + x2 = 0.94140625

Factor a perfect square on the left side:
(x + 0.5625)(x + 0.5625) = 0.94140625

Calculate the square root of the right side: 0.970260919

Break this problem into two subproblems by setting 
(x + 0.5625) equal to 0.970260919 and -0.970260919.


Subproblem 1
x + 0.5625 = 0.970260919

Simplifying
x + 0.5625 = 0.970260919

Reorder the terms:
0.5625 + x = 0.970260919

Solving
0.5625 + x = 0.970260919

Solving for variable 'x'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + x = 0.970260919 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + x = 0.970260919 + -0.5625
x = 0.970260919 + -0.5625

Combine like terms: 0.970260919 + -0.5625 = 0.407760919
x = 0.407760919

Simplifying
x = 0.407760919


Subproblem 2
x + 0.5625 = -0.970260919

Simplifying
x + 0.5625 = -0.970260919

Reorder the terms:
0.5625 + x = -0.970260919

Solving
0.5625 + x = -0.970260919

Solving for variable 'x'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + x = -0.970260919 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + x = -0.970260919 + -0.5625
x = -0.970260919 + -0.5625

Combine like terms: -0.970260919 + -0.5625 = -1.532760919
x = -1.532760919

Simplifying
x = -1.532760919


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.407760919, -1.532760919}

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