3x^2-20x-36=0

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Solution for 3x^2-20x-36=0 equation: 


Simplifying
3x2 + -20x + -36 = 0

Reorder the terms:
-36 + -20x + 3x2 = 0

Solving
-36 + -20x + 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 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -6.666666667x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -6.666666667x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -6.666666667x + x2 = 0 + 12
-6.666666667x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-6.666666667x + x2 = 12

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = 12 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 12 + 11.11111112

Combine like terms: 12 + 11.11111112 = 23.11111112
11.11111112 + -6.666666667x + x2 = 23.11111112

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 23.11111112

Calculate the square root of the right side: 4.807401702

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 4.807401702 and -4.807401702.


Subproblem 1
x + -3.333333334 = 4.807401702

Simplifying
x + -3.333333334 = 4.807401702

Reorder the terms:
-3.333333334 + x = 4.807401702

Solving
-3.333333334 + x = 4.807401702

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 4.807401702 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 4.807401702 + 3.333333334
x = 4.807401702 + 3.333333334

Combine like terms: 4.807401702 + 3.333333334 = 8.140735036
x = 8.140735036

Simplifying
x = 8.140735036


Subproblem 2
x + -3.333333334 = -4.807401702

Simplifying
x + -3.333333334 = -4.807401702

Reorder the terms:
-3.333333334 + x = -4.807401702

Solving
-3.333333334 + x = -4.807401702

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -4.807401702 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -4.807401702 + 3.333333334
x = -4.807401702 + 3.333333334

Combine like terms: -4.807401702 + 3.333333334 = -1.474068368
x = -1.474068368

Simplifying
x = -1.474068368


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.140735036, -1.474068368}

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