9x^2-40x-65=0

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Solution for 9x^2-40x-65=0 equation: 


Simplifying
9x2 + -40x + -65 = 0

Reorder the terms:
-65 + -40x + 9x2 = 0

Solving
-65 + -40x + 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'.
-7.222222222 + -4.444444444x + x2 = 0

Move the constant term to the right:

Add '7.222222222' to each side of the equation.
-7.222222222 + -4.444444444x + 7.222222222 + x2 = 0 + 7.222222222

Reorder the terms:
-7.222222222 + 7.222222222 + -4.444444444x + x2 = 0 + 7.222222222

Combine like terms: -7.222222222 + 7.222222222 = 0.000000000
0.000000000 + -4.444444444x + x2 = 0 + 7.222222222
-4.444444444x + x2 = 0 + 7.222222222

Combine like terms: 0 + 7.222222222 = 7.222222222
-4.444444444x + x2 = 7.222222222

The x term is -4.444444444x.  Take half its coefficient (-2.222222222).
Square it (4.938271604) and add it to both sides.

Add '4.938271604' to each side of the equation.
-4.444444444x + 4.938271604 + x2 = 7.222222222 + 4.938271604

Reorder the terms:
4.938271604 + -4.444444444x + x2 = 7.222222222 + 4.938271604

Combine like terms: 7.222222222 + 4.938271604 = 12.160493826
4.938271604 + -4.444444444x + x2 = 12.160493826

Factor a perfect square on the left side:
(x + -2.222222222)(x + -2.222222222) = 12.160493826

Calculate the square root of the right side: 3.487189961

Break this problem into two subproblems by setting 
(x + -2.222222222) equal to 3.487189961 and -3.487189961.


Subproblem 1
x + -2.222222222 = 3.487189961

Simplifying
x + -2.222222222 = 3.487189961

Reorder the terms:
-2.222222222 + x = 3.487189961

Solving
-2.222222222 + x = 3.487189961

Solving for variable 'x'.

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

Add '2.222222222' to each side of the equation.
-2.222222222 + 2.222222222 + x = 3.487189961 + 2.222222222

Combine like terms: -2.222222222 + 2.222222222 = 0.000000000
0.000000000 + x = 3.487189961 + 2.222222222
x = 3.487189961 + 2.222222222

Combine like terms: 3.487189961 + 2.222222222 = 5.709412183
x = 5.709412183

Simplifying
x = 5.709412183


Subproblem 2
x + -2.222222222 = -3.487189961

Simplifying
x + -2.222222222 = -3.487189961

Reorder the terms:
-2.222222222 + x = -3.487189961

Solving
-2.222222222 + x = -3.487189961

Solving for variable 'x'.

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

Add '2.222222222' to each side of the equation.
-2.222222222 + 2.222222222 + x = -3.487189961 + 2.222222222

Combine like terms: -2.222222222 + 2.222222222 = 0.000000000
0.000000000 + x = -3.487189961 + 2.222222222
x = -3.487189961 + 2.222222222

Combine like terms: -3.487189961 + 2.222222222 = -1.264967739
x = -1.264967739

Simplifying
x = -1.264967739


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.709412183, -1.264967739}

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