3x^2-46x-120=0

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Solution for 3x^2-46x-120=0 equation: 


Simplifying
3x2 + -46x + -120 = 0

Reorder the terms:
-120 + -46x + 3x2 = 0

Solving
-120 + -46x + 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 + -15.33333333x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -15.33333333x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -15.33333333x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -15.33333333x + x2 = 0 + 40
-15.33333333x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-15.33333333x + x2 = 40

The x term is -15.33333333x.  Take half its coefficient (-7.666666665).
Square it (58.77777775) and add it to both sides.

Add '58.77777775' to each side of the equation.
-15.33333333x + 58.77777775 + x2 = 40 + 58.77777775

Reorder the terms:
58.77777775 + -15.33333333x + x2 = 40 + 58.77777775

Combine like terms: 40 + 58.77777775 = 98.77777775
58.77777775 + -15.33333333x + x2 = 98.77777775

Factor a perfect square on the left side:
(x + -7.666666665)(x + -7.666666665) = 98.77777775

Calculate the square root of the right side: 9.938701009

Break this problem into two subproblems by setting 
(x + -7.666666665) equal to 9.938701009 and -9.938701009.


Subproblem 1
x + -7.666666665 = 9.938701009

Simplifying
x + -7.666666665 = 9.938701009

Reorder the terms:
-7.666666665 + x = 9.938701009

Solving
-7.666666665 + x = 9.938701009

Solving for variable 'x'.

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

Add '7.666666665' to each side of the equation.
-7.666666665 + 7.666666665 + x = 9.938701009 + 7.666666665

Combine like terms: -7.666666665 + 7.666666665 = 0.000000000
0.000000000 + x = 9.938701009 + 7.666666665
x = 9.938701009 + 7.666666665

Combine like terms: 9.938701009 + 7.666666665 = 17.605367674
x = 17.605367674

Simplifying
x = 17.605367674


Subproblem 2
x + -7.666666665 = -9.938701009

Simplifying
x + -7.666666665 = -9.938701009

Reorder the terms:
-7.666666665 + x = -9.938701009

Solving
-7.666666665 + x = -9.938701009

Solving for variable 'x'.

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

Add '7.666666665' to each side of the equation.
-7.666666665 + 7.666666665 + x = -9.938701009 + 7.666666665

Combine like terms: -7.666666665 + 7.666666665 = 0.000000000
0.000000000 + x = -9.938701009 + 7.666666665
x = -9.938701009 + 7.666666665

Combine like terms: -9.938701009 + 7.666666665 = -2.272034344
x = -2.272034344

Simplifying
x = -2.272034344


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.605367674, -2.272034344}

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