9x^2+8x-5=0

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

Simplifying
9x2 + 8x + -5 = 0

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

Solving
-5 + 8x + 9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-0.5555555556 + 0.8888888889x + x2 = 0

Move the constant term to the right:

Add '0.5555555556' to each side of the equation.
-0.5555555556 + 0.8888888889x + 0.5555555556 + x2 = 0 + 0.5555555556

Reorder the terms:
-0.5555555556 + 0.5555555556 + 0.8888888889x + x2 = 0 + 0.5555555556

Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000
0.0000000000 + 0.8888888889x + x2 = 0 + 0.5555555556
0.8888888889x + x2 = 0 + 0.5555555556

Combine like terms: 0 + 0.5555555556 = 0.5555555556
0.8888888889x + x2 = 0.5555555556

The x term is 0.8888888889x.  Take half its coefficient (0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
0.8888888889x + 0.1975308642 + x2 = 0.5555555556 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889x + x2 = 0.5555555556 + 0.1975308642

Combine like terms: 0.5555555556 + 0.1975308642 = 0.7530864198
0.1975308642 + 0.8888888889x + x2 = 0.7530864198

Factor a perfect square on the left side:
(x + 0.4444444445)(x + 0.4444444445) = 0.7530864198

Calculate the square root of the right side: 0.86780552

Break this problem into two subproblems by setting 
(x + 0.4444444445) equal to 0.86780552 and -0.86780552.

Subproblem 1
x + 0.4444444445 = 0.86780552

Simplifying
x + 0.4444444445 = 0.86780552

Reorder the terms:
0.4444444445 + x = 0.86780552

Solving
0.4444444445 + x = 0.86780552

Solving for variable 'x'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + x = 0.86780552 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = 0.86780552 + -0.4444444445
x = 0.86780552 + -0.4444444445

Combine like terms: 0.86780552 + -0.4444444445 = 0.4233610755
x = 0.4233610755

Simplifying
x = 0.4233610755

Subproblem 2
x + 0.4444444445 = -0.86780552

Simplifying
x + 0.4444444445 = -0.86780552

Reorder the terms:
0.4444444445 + x = -0.86780552

Solving
0.4444444445 + x = -0.86780552

Solving for variable 'x'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + x = -0.86780552 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = -0.86780552 + -0.4444444445
x = -0.86780552 + -0.4444444445

Combine like terms: -0.86780552 + -0.4444444445 = -1.3122499645
x = -1.3122499645

Simplifying
x = -1.3122499645

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4233610755, -1.3122499645}