9x^2-5x-1=0

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Solution for 9x^2-5x-1=0 equation: 


Simplifying
9x2 + -5x + -1 = 0

Reorder the terms:
-1 + -5x + 9x2 = 0

Solving
-1 + -5x + 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 + -0.5555555556x + x2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + -0.5555555556x + 0.1111111111 + x2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + -0.5555555556x + x2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + -0.5555555556x + x2 = 0 + 0.1111111111
-0.5555555556x + x2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
-0.5555555556x + x2 = 0.1111111111

The x term is -0.5555555556x.  Take half its coefficient (-0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
-0.5555555556x + 0.07716049384 + x2 = 0.1111111111 + 0.07716049384

Reorder the terms:
0.07716049384 + -0.5555555556x + x2 = 0.1111111111 + 0.07716049384

Combine like terms: 0.1111111111 + 0.07716049384 = 0.18827160494
0.07716049384 + -0.5555555556x + x2 = 0.18827160494

Factor a perfect square on the left side:
(x + -0.2777777778)(x + -0.2777777778) = 0.18827160494

Calculate the square root of the right side: 0.43390276

Break this problem into two subproblems by setting 
(x + -0.2777777778) equal to 0.43390276 and -0.43390276.


Subproblem 1
x + -0.2777777778 = 0.43390276

Simplifying
x + -0.2777777778 = 0.43390276

Reorder the terms:
-0.2777777778 + x = 0.43390276

Solving
-0.2777777778 + x = 0.43390276

Solving for variable 'x'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + x = 0.43390276 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + x = 0.43390276 + 0.2777777778
x = 0.43390276 + 0.2777777778

Combine like terms: 0.43390276 + 0.2777777778 = 0.7116805378
x = 0.7116805378

Simplifying
x = 0.7116805378


Subproblem 2
x + -0.2777777778 = -0.43390276

Simplifying
x + -0.2777777778 = -0.43390276

Reorder the terms:
-0.2777777778 + x = -0.43390276

Solving
-0.2777777778 + x = -0.43390276

Solving for variable 'x'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + x = -0.43390276 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + x = -0.43390276 + 0.2777777778
x = -0.43390276 + 0.2777777778

Combine like terms: -0.43390276 + 0.2777777778 = -0.1561249822
x = -0.1561249822

Simplifying
x = -0.1561249822


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7116805378, -0.1561249822}

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