9x^2+16x-8=0

Solution for 9x^2+16x-8=0 equation:

Simplifying
9x2 + 16x + -8 = 0

Reorder the terms:
-8 + 16x + 9x2 = 0

Solving
-8 + 16x + 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'.
-0.8888888889 + 1.777777778x + x2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + 1.777777778x + 0.8888888889 + x2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + 1.777777778x + x2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + 1.777777778x + x2 = 0 + 0.8888888889
1.777777778x + x2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
1.777777778x + x2 = 0.8888888889

The x term is 1.777777778x.  Take half its coefficient (0.888888889).
Square it (0.7901234570) and add it to both sides.

Add '0.7901234570' to each side of the equation.
1.777777778x + 0.7901234570 + x2 = 0.8888888889 + 0.7901234570

Reorder the terms:
0.7901234570 + 1.777777778x + x2 = 0.8888888889 + 0.7901234570

Combine like terms: 0.8888888889 + 0.7901234570 = 1.6790123459
0.7901234570 + 1.777777778x + x2 = 1.6790123459

Factor a perfect square on the left side:
(x + 0.888888889)(x + 0.888888889) = 1.6790123459

Calculate the square root of the right side: 1.295767088

Break this problem into two subproblems by setting 
(x + 0.888888889) equal to 1.295767088 and -1.295767088.

Subproblem 1
x + 0.888888889 = 1.295767088

Simplifying
x + 0.888888889 = 1.295767088

Reorder the terms:
0.888888889 + x = 1.295767088

Solving
0.888888889 + x = 1.295767088

Solving for variable 'x'.

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

Add '-0.888888889' to each side of the equation.
0.888888889 + -0.888888889 + x = 1.295767088 + -0.888888889

Combine like terms: 0.888888889 + -0.888888889 = 0.000000000
0.000000000 + x = 1.295767088 + -0.888888889
x = 1.295767088 + -0.888888889

Combine like terms: 1.295767088 + -0.888888889 = 0.406878199
x = 0.406878199

Simplifying
x = 0.406878199

Subproblem 2
x + 0.888888889 = -1.295767088

Simplifying
x + 0.888888889 = -1.295767088

Reorder the terms:
0.888888889 + x = -1.295767088

Solving
0.888888889 + x = -1.295767088

Solving for variable 'x'.

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

Add '-0.888888889' to each side of the equation.
0.888888889 + -0.888888889 + x = -1.295767088 + -0.888888889

Combine like terms: 0.888888889 + -0.888888889 = 0.000000000
0.000000000 + x = -1.295767088 + -0.888888889
x = -1.295767088 + -0.888888889

Combine like terms: -1.295767088 + -0.888888889 = -2.184655977
x = -2.184655977

Simplifying
x = -2.184655977

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.406878199, -2.184655977}