3x^2-55x-300=0

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Solution for 3x^2-55x-300=0 equation: 


Simplifying
3x2 + -55x + -300 = 0

Reorder the terms:
-300 + -55x + 3x2 = 0

Solving
-300 + -55x + 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'.
-100 + -18.33333333x + x2 = 0

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -18.33333333x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + -18.33333333x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -18.33333333x + x2 = 0 + 100
-18.33333333x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
-18.33333333x + x2 = 100

The x term is -18.33333333x.  Take half its coefficient (-9.166666665).
Square it (84.02777775) and add it to both sides.

Add '84.02777775' to each side of the equation.
-18.33333333x + 84.02777775 + x2 = 100 + 84.02777775

Reorder the terms:
84.02777775 + -18.33333333x + x2 = 100 + 84.02777775

Combine like terms: 100 + 84.02777775 = 184.02777775
84.02777775 + -18.33333333x + x2 = 184.02777775

Factor a perfect square on the left side:
(x + -9.166666665)(x + -9.166666665) = 184.02777775

Calculate the square root of the right side: 13.565683829

Break this problem into two subproblems by setting 
(x + -9.166666665) equal to 13.565683829 and -13.565683829.


Subproblem 1
x + -9.166666665 = 13.565683829

Simplifying
x + -9.166666665 = 13.565683829

Reorder the terms:
-9.166666665 + x = 13.565683829

Solving
-9.166666665 + x = 13.565683829

Solving for variable 'x'.

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

Add '9.166666665' to each side of the equation.
-9.166666665 + 9.166666665 + x = 13.565683829 + 9.166666665

Combine like terms: -9.166666665 + 9.166666665 = 0.000000000
0.000000000 + x = 13.565683829 + 9.166666665
x = 13.565683829 + 9.166666665

Combine like terms: 13.565683829 + 9.166666665 = 22.732350494
x = 22.732350494

Simplifying
x = 22.732350494


Subproblem 2
x + -9.166666665 = -13.565683829

Simplifying
x + -9.166666665 = -13.565683829

Reorder the terms:
-9.166666665 + x = -13.565683829

Solving
-9.166666665 + x = -13.565683829

Solving for variable 'x'.

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

Add '9.166666665' to each side of the equation.
-9.166666665 + 9.166666665 + x = -13.565683829 + 9.166666665

Combine like terms: -9.166666665 + 9.166666665 = 0.000000000
0.000000000 + x = -13.565683829 + 9.166666665
x = -13.565683829 + 9.166666665

Combine like terms: -13.565683829 + 9.166666665 = -4.399017164
x = -4.399017164

Simplifying
x = -4.399017164


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.732350494, -4.399017164}

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