3x^2-34x-2320=0

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Solution for 3x^2-34x-2320=0 equation: 


Simplifying
3x2 + -34x + -2320 = 0

Reorder the terms:
-2320 + -34x + 3x2 = 0

Solving
-2320 + -34x + 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'.
-773.3333333 + -11.33333333x + x2 = 0

Move the constant term to the right:

Add '773.3333333' to each side of the equation.
-773.3333333 + -11.33333333x + 773.3333333 + x2 = 0 + 773.3333333

Reorder the terms:
-773.3333333 + 773.3333333 + -11.33333333x + x2 = 0 + 773.3333333

Combine like terms: -773.3333333 + 773.3333333 = 0.0000000
0.0000000 + -11.33333333x + x2 = 0 + 773.3333333
-11.33333333x + x2 = 0 + 773.3333333

Combine like terms: 0 + 773.3333333 = 773.3333333
-11.33333333x + x2 = 773.3333333

The x term is -11.33333333x.  Take half its coefficient (-5.666666665).
Square it (32.11111109) and add it to both sides.

Add '32.11111109' to each side of the equation.
-11.33333333x + 32.11111109 + x2 = 773.3333333 + 32.11111109

Reorder the terms:
32.11111109 + -11.33333333x + x2 = 773.3333333 + 32.11111109

Combine like terms: 773.3333333 + 32.11111109 = 805.44444439
32.11111109 + -11.33333333x + x2 = 805.44444439

Factor a perfect square on the left side:
(x + -5.666666665)(x + -5.666666665) = 805.44444439

Calculate the square root of the right side: 28.380353141

Break this problem into two subproblems by setting 
(x + -5.666666665) equal to 28.380353141 and -28.380353141.


Subproblem 1
x + -5.666666665 = 28.380353141

Simplifying
x + -5.666666665 = 28.380353141

Reorder the terms:
-5.666666665 + x = 28.380353141

Solving
-5.666666665 + x = 28.380353141

Solving for variable 'x'.

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

Add '5.666666665' to each side of the equation.
-5.666666665 + 5.666666665 + x = 28.380353141 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = 28.380353141 + 5.666666665
x = 28.380353141 + 5.666666665

Combine like terms: 28.380353141 + 5.666666665 = 34.047019806
x = 34.047019806

Simplifying
x = 34.047019806


Subproblem 2
x + -5.666666665 = -28.380353141

Simplifying
x + -5.666666665 = -28.380353141

Reorder the terms:
-5.666666665 + x = -28.380353141

Solving
-5.666666665 + x = -28.380353141

Solving for variable 'x'.

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

Add '5.666666665' to each side of the equation.
-5.666666665 + 5.666666665 + x = -28.380353141 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = -28.380353141 + 5.666666665
x = -28.380353141 + 5.666666665

Combine like terms: -28.380353141 + 5.666666665 = -22.713686476
x = -22.713686476

Simplifying
x = -22.713686476


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.047019806, -22.713686476}

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