3x^2-8x-120=0

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Solution for 3x^2-8x-120=0 equation: 


Simplifying
3x2 + -8x + -120 = 0

Reorder the terms:
-120 + -8x + 3x2 = 0

Solving
-120 + -8x + 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'.
-40 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -2.666666667x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -2.666666667x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -2.666666667x + x2 = 0 + 40
-2.666666667x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-2.666666667x + x2 = 40

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 40 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 40 + 1.777777780

Combine like terms: 40 + 1.777777780 = 41.77777778
1.777777780 + -2.666666667x + x2 = 41.77777778

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 41.77777778

Calculate the square root of the right side: 6.463573143

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 6.463573143 and -6.463573143.


Subproblem 1
x + -1.333333334 = 6.463573143

Simplifying
x + -1.333333334 = 6.463573143

Reorder the terms:
-1.333333334 + x = 6.463573143

Solving
-1.333333334 + x = 6.463573143

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 6.463573143 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 6.463573143 + 1.333333334
x = 6.463573143 + 1.333333334

Combine like terms: 6.463573143 + 1.333333334 = 7.796906477
x = 7.796906477

Simplifying
x = 7.796906477


Subproblem 2
x + -1.333333334 = -6.463573143

Simplifying
x + -1.333333334 = -6.463573143

Reorder the terms:
-1.333333334 + x = -6.463573143

Solving
-1.333333334 + x = -6.463573143

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -6.463573143 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -6.463573143 + 1.333333334
x = -6.463573143 + 1.333333334

Combine like terms: -6.463573143 + 1.333333334 = -5.130239809
x = -5.130239809

Simplifying
x = -5.130239809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.796906477, -5.130239809}

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