1.5x^2-20x-31=0

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Solution for 1.5x^2-20x-31=0 equation: 


Simplifying
1.5x2 + -20x + -31 = 0

Reorder the terms:
-31 + -20x + 1.5x2 = 0

Solving
-31 + -20x + 1.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.5'.
-20.66666667 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '20.66666667' to each side of the equation.
-20.66666667 + -13.33333333x + 20.66666667 + x2 = 0 + 20.66666667

Reorder the terms:
-20.66666667 + 20.66666667 + -13.33333333x + x2 = 0 + 20.66666667

Combine like terms: -20.66666667 + 20.66666667 = 0.00000000
0.00000000 + -13.33333333x + x2 = 0 + 20.66666667
-13.33333333x + x2 = 0 + 20.66666667

Combine like terms: 0 + 20.66666667 = 20.66666667
-13.33333333x + x2 = 20.66666667

The x term is -13.33333333x.  Take half its coefficient (-6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
-13.33333333x + 44.44444442 + x2 = 20.66666667 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = 20.66666667 + 44.44444442

Combine like terms: 20.66666667 + 44.44444442 = 65.11111109
44.44444442 + -13.33333333x + x2 = 65.11111109

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = 65.11111109

Calculate the square root of the right side: 8.069145623

Break this problem into two subproblems by setting 
(x + -6.666666665) equal to 8.069145623 and -8.069145623.


Subproblem 1
x + -6.666666665 = 8.069145623

Simplifying
x + -6.666666665 = 8.069145623

Reorder the terms:
-6.666666665 + x = 8.069145623

Solving
-6.666666665 + x = 8.069145623

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = 8.069145623 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = 8.069145623 + 6.666666665
x = 8.069145623 + 6.666666665

Combine like terms: 8.069145623 + 6.666666665 = 14.735812288
x = 14.735812288

Simplifying
x = 14.735812288


Subproblem 2
x + -6.666666665 = -8.069145623

Simplifying
x + -6.666666665 = -8.069145623

Reorder the terms:
-6.666666665 + x = -8.069145623

Solving
-6.666666665 + x = -8.069145623

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = -8.069145623 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = -8.069145623 + 6.666666665
x = -8.069145623 + 6.666666665

Combine like terms: -8.069145623 + 6.666666665 = -1.402478958
x = -1.402478958

Simplifying
x = -1.402478958


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.735812288, -1.402478958}

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