-8x^2+5x+9=0

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


Simplifying
-8x2 + 5x + 9 = 0

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

Solving
9 + 5x + -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 + -0.625x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is -0.625x.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625x + 0.09765625 + x2 = 1.125 + 0.09765625

Reorder the terms:
0.09765625 + -0.625x + x2 = 1.125 + 0.09765625

Combine like terms: 1.125 + 0.09765625 = 1.22265625
0.09765625 + -0.625x + x2 = 1.22265625

Factor a perfect square on the left side:
(x + -0.3125)(x + -0.3125) = 1.22265625

Calculate the square root of the right side: 1.105737876

Break this problem into two subproblems by setting 
(x + -0.3125) equal to 1.105737876 and -1.105737876.


Subproblem 1
x + -0.3125 = 1.105737876

Simplifying
x + -0.3125 = 1.105737876

Reorder the terms:
-0.3125 + x = 1.105737876

Solving
-0.3125 + x = 1.105737876

Solving for variable 'x'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + x = 1.105737876 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + x = 1.105737876 + 0.3125
x = 1.105737876 + 0.3125

Combine like terms: 1.105737876 + 0.3125 = 1.418237876
x = 1.418237876

Simplifying
x = 1.418237876


Subproblem 2
x + -0.3125 = -1.105737876

Simplifying
x + -0.3125 = -1.105737876

Reorder the terms:
-0.3125 + x = -1.105737876

Solving
-0.3125 + x = -1.105737876

Solving for variable 'x'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + x = -1.105737876 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + x = -1.105737876 + 0.3125
x = -1.105737876 + 0.3125

Combine like terms: -1.105737876 + 0.3125 = -0.793237876
x = -0.793237876

Simplifying
x = -0.793237876


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.418237876, -0.793237876}

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