3x^2-20x-16=0

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Solution for 3x^2-20x-16=0 equation: 


Simplifying
3x2 + -20x + -16 = 0

Reorder the terms:
-16 + -20x + 3x2 = 0

Solving
-16 + -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'.
-5.333333333 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -6.666666667x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -6.666666667x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + 5.333333333
-6.666666667x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-6.666666667x + x2 = 5.333333333

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 = 5.333333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 5.333333333 + 11.11111112

Combine like terms: 5.333333333 + 11.11111112 = 16.444444453
11.11111112 + -6.666666667x + x2 = 16.444444453

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 16.444444453

Calculate the square root of the right side: 4.055175021

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 4.055175021 and -4.055175021.


Subproblem 1
x + -3.333333334 = 4.055175021

Simplifying
x + -3.333333334 = 4.055175021

Reorder the terms:
-3.333333334 + x = 4.055175021

Solving
-3.333333334 + x = 4.055175021

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 = 4.055175021 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 4.055175021 + 3.333333334
x = 4.055175021 + 3.333333334

Combine like terms: 4.055175021 + 3.333333334 = 7.388508355
x = 7.388508355

Simplifying
x = 7.388508355


Subproblem 2
x + -3.333333334 = -4.055175021

Simplifying
x + -3.333333334 = -4.055175021

Reorder the terms:
-3.333333334 + x = -4.055175021

Solving
-3.333333334 + x = -4.055175021

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 = -4.055175021 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -4.055175021 + 3.333333334
x = -4.055175021 + 3.333333334

Combine like terms: -4.055175021 + 3.333333334 = -0.721841687
x = -0.721841687

Simplifying
x = -0.721841687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.388508355, -0.721841687}

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