3x^2-65x-50=0

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Solution for 3x^2-65x-50=0 equation: 


Simplifying
3x2 + -65x + -50 = 0

Reorder the terms:
-50 + -65x + 3x2 = 0

Solving
-50 + -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'.
-16.66666667 + -21.66666667x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + -21.66666667x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + -21.66666667x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + -21.66666667x + x2 = 0 + 16.66666667
-21.66666667x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
-21.66666667x + x2 = 16.66666667

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 = 16.66666667 + 117.3611113

Reorder the terms:
117.3611113 + -21.66666667x + x2 = 16.66666667 + 117.3611113

Combine like terms: 16.66666667 + 117.3611113 = 134.02777797
117.3611113 + -21.66666667x + x2 = 134.02777797

Factor a perfect square on the left side:
(x + -10.83333334)(x + -10.83333334) = 134.02777797

Calculate the square root of the right side: 11.577036666

Break this problem into two subproblems by setting 
(x + -10.83333334) equal to 11.577036666 and -11.577036666.


Subproblem 1
x + -10.83333334 = 11.577036666

Simplifying
x + -10.83333334 = 11.577036666

Reorder the terms:
-10.83333334 + x = 11.577036666

Solving
-10.83333334 + x = 11.577036666

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 = 11.577036666 + 10.83333334

Combine like terms: -10.83333334 + 10.83333334 = 0.00000000
0.00000000 + x = 11.577036666 + 10.83333334
x = 11.577036666 + 10.83333334

Combine like terms: 11.577036666 + 10.83333334 = 22.410370006
x = 22.410370006

Simplifying
x = 22.410370006


Subproblem 2
x + -10.83333334 = -11.577036666

Simplifying
x + -10.83333334 = -11.577036666

Reorder the terms:
-10.83333334 + x = -11.577036666

Solving
-10.83333334 + x = -11.577036666

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 = -11.577036666 + 10.83333334

Combine like terms: -10.83333334 + 10.83333334 = 0.00000000
0.00000000 + x = -11.577036666 + 10.83333334
x = -11.577036666 + 10.83333334

Combine like terms: -11.577036666 + 10.83333334 = -0.743703326
x = -0.743703326

Simplifying
x = -0.743703326


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.410370006, -0.743703326}

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