9x^2+10x-1=0

Solution for 9x^2+10x-1=0 equation:

Simplifying
9x2 + 10x + -1 = 0

Reorder the terms:
-1 + 10x + 9x2 = 0

Solving
-1 + 10x + 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'.
-0.1111111111 + 1.111111111x + x2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 1.111111111x + 0.1111111111 + x2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + 1.111111111x + x2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + 1.111111111x + x2 = 0 + 0.1111111111
1.111111111x + x2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
1.111111111x + x2 = 0.1111111111

The x term is 1.111111111x.  Take half its coefficient (0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
1.111111111x + 0.3086419752 + x2 = 0.1111111111 + 0.3086419752

Reorder the terms:
0.3086419752 + 1.111111111x + x2 = 0.1111111111 + 0.3086419752

Combine like terms: 0.1111111111 + 0.3086419752 = 0.4197530863
0.3086419752 + 1.111111111x + x2 = 0.4197530863

Factor a perfect square on the left side:
(x + 0.5555555555)(x + 0.5555555555) = 0.4197530863

Calculate the square root of the right side: 0.647883544

Break this problem into two subproblems by setting 
(x + 0.5555555555) equal to 0.647883544 and -0.647883544.

Subproblem 1
x + 0.5555555555 = 0.647883544

Simplifying
x + 0.5555555555 = 0.647883544

Reorder the terms:
0.5555555555 + x = 0.647883544

Solving
0.5555555555 + x = 0.647883544

Solving for variable 'x'.

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

Add '-0.5555555555' to each side of the equation.
0.5555555555 + -0.5555555555 + x = 0.647883544 + -0.5555555555

Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000
0.0000000000 + x = 0.647883544 + -0.5555555555
x = 0.647883544 + -0.5555555555

Combine like terms: 0.647883544 + -0.5555555555 = 0.0923279885
x = 0.0923279885

Simplifying
x = 0.0923279885

Subproblem 2
x + 0.5555555555 = -0.647883544

Simplifying
x + 0.5555555555 = -0.647883544

Reorder the terms:
0.5555555555 + x = -0.647883544

Solving
0.5555555555 + x = -0.647883544

Solving for variable 'x'.

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

Add '-0.5555555555' to each side of the equation.
0.5555555555 + -0.5555555555 + x = -0.647883544 + -0.5555555555

Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000
0.0000000000 + x = -0.647883544 + -0.5555555555
x = -0.647883544 + -0.5555555555

Combine like terms: -0.647883544 + -0.5555555555 = -1.2034390995
x = -1.2034390995

Simplifying
x = -1.2034390995

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0923279885, -1.2034390995}