3x^2-65x-36=0

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Solution for 3x^2-65x-36=0 equation: 


Simplifying
3x2 + -65x + -36 = 0

Reorder the terms:
-36 + -65x + 3x2 = 0

Solving
-36 + -65x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-12 + -21.66666667x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -21.66666667x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -21.66666667x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -21.66666667x + x2 = 0 + 12
-21.66666667x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-21.66666667x + x2 = 12

The x term is -21.66666667x.  Take half its coefficient (-10.83333334).
Square it (117.3611113) and add it to both sides.

Add '117.3611113' to each side of the equation.
-21.66666667x + 117.3611113 + x2 = 12 + 117.3611113

Reorder the terms:
117.3611113 + -21.66666667x + x2 = 12 + 117.3611113

Combine like terms: 12 + 117.3611113 = 129.3611113
117.3611113 + -21.66666667x + x2 = 129.3611113

Factor a perfect square on the left side:
(x + -10.83333334)(x + -10.83333334) = 129.3611113

Calculate the square root of the right side: 11.373702621

Break this problem into two subproblems by setting 
(x + -10.83333334) equal to 11.373702621 and -11.373702621.


Subproblem 1
x + -10.83333334 = 11.373702621

Simplifying
x + -10.83333334 = 11.373702621

Reorder the terms:
-10.83333334 + x = 11.373702621

Solving
-10.83333334 + x = 11.373702621

Solving for variable 'x'.

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

Add '10.83333334' to each side of the equation.
-10.83333334 + 10.83333334 + x = 11.373702621 + 10.83333334

Combine like terms: -10.83333334 + 10.83333334 = 0.00000000
0.00000000 + x = 11.373702621 + 10.83333334
x = 11.373702621 + 10.83333334

Combine like terms: 11.373702621 + 10.83333334 = 22.207035961
x = 22.207035961

Simplifying
x = 22.207035961


Subproblem 2
x + -10.83333334 = -11.373702621

Simplifying
x + -10.83333334 = -11.373702621

Reorder the terms:
-10.83333334 + x = -11.373702621

Solving
-10.83333334 + x = -11.373702621

Solving for variable 'x'.

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

Add '10.83333334' to each side of the equation.
-10.83333334 + 10.83333334 + x = -11.373702621 + 10.83333334

Combine like terms: -10.83333334 + 10.83333334 = 0.00000000
0.00000000 + x = -11.373702621 + 10.83333334
x = -11.373702621 + 10.83333334

Combine like terms: -11.373702621 + 10.83333334 = -0.540369281
x = -0.540369281

Simplifying
x = -0.540369281


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.207035961, -0.540369281}

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