9x^2+6x-5=0

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Solution for 9x^2+6x-5=0 equation: 


Simplifying
9x2 + 6x + -5 = 0

Reorder the terms:
-5 + 6x + 9x2 = 0

Solving
-5 + 6x + 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 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.5555555556' to each side of the equation.
-0.5555555556 + 0.6666666667x + 0.5555555556 + x2 = 0 + 0.5555555556

Reorder the terms:
-0.5555555556 + 0.5555555556 + 0.6666666667x + x2 = 0 + 0.5555555556

Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000
0.0000000000 + 0.6666666667x + x2 = 0 + 0.5555555556
0.6666666667x + x2 = 0 + 0.5555555556

Combine like terms: 0 + 0.5555555556 = 0.5555555556
0.6666666667x + x2 = 0.5555555556

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 0.5555555556 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.5555555556 + 0.1111111112

Combine like terms: 0.5555555556 + 0.1111111112 = 0.6666666668
0.1111111112 + 0.6666666667x + x2 = 0.6666666668

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.6666666668

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.816496581 and -0.816496581.


Subproblem 1
x + 0.3333333334 = 0.816496581

Simplifying
x + 0.3333333334 = 0.816496581

Reorder the terms:
0.3333333334 + x = 0.816496581

Solving
0.3333333334 + x = 0.816496581

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.816496581 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.816496581 + -0.3333333334
x = 0.816496581 + -0.3333333334

Combine like terms: 0.816496581 + -0.3333333334 = 0.4831632476
x = 0.4831632476

Simplifying
x = 0.4831632476


Subproblem 2
x + 0.3333333334 = -0.816496581

Simplifying
x + 0.3333333334 = -0.816496581

Reorder the terms:
0.3333333334 + x = -0.816496581

Solving
0.3333333334 + x = -0.816496581

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.816496581 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.816496581 + -0.3333333334
x = -0.816496581 + -0.3333333334

Combine like terms: -0.816496581 + -0.3333333334 = -1.1498299144
x = -1.1498299144

Simplifying
x = -1.1498299144


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4831632476, -1.1498299144}

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