3x^2-34x+64=0

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Solution for 3x^2-34x+64=0 equation: 


Simplifying
3x2 + -34x + 64 = 0

Reorder the terms:
64 + -34x + 3x2 = 0

Solving
64 + -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'.
21.33333333 + -11.33333333x + x2 = 0

Move the constant term to the right:

Add '-21.33333333' to each side of the equation.
21.33333333 + -11.33333333x + -21.33333333 + x2 = 0 + -21.33333333

Reorder the terms:
21.33333333 + -21.33333333 + -11.33333333x + x2 = 0 + -21.33333333

Combine like terms: 21.33333333 + -21.33333333 = 0.00000000
0.00000000 + -11.33333333x + x2 = 0 + -21.33333333
-11.33333333x + x2 = 0 + -21.33333333

Combine like terms: 0 + -21.33333333 = -21.33333333
-11.33333333x + x2 = -21.33333333

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 = -21.33333333 + 32.11111109

Reorder the terms:
32.11111109 + -11.33333333x + x2 = -21.33333333 + 32.11111109

Combine like terms: -21.33333333 + 32.11111109 = 10.77777776
32.11111109 + -11.33333333x + x2 = 10.77777776

Factor a perfect square on the left side:
(x + -5.666666665)(x + -5.666666665) = 10.77777776

Calculate the square root of the right side: 3.282952598

Break this problem into two subproblems by setting 
(x + -5.666666665) equal to 3.282952598 and -3.282952598.


Subproblem 1
x + -5.666666665 = 3.282952598

Simplifying
x + -5.666666665 = 3.282952598

Reorder the terms:
-5.666666665 + x = 3.282952598

Solving
-5.666666665 + x = 3.282952598

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 = 3.282952598 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = 3.282952598 + 5.666666665
x = 3.282952598 + 5.666666665

Combine like terms: 3.282952598 + 5.666666665 = 8.949619263
x = 8.949619263

Simplifying
x = 8.949619263


Subproblem 2
x + -5.666666665 = -3.282952598

Simplifying
x + -5.666666665 = -3.282952598

Reorder the terms:
-5.666666665 + x = -3.282952598

Solving
-5.666666665 + x = -3.282952598

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 = -3.282952598 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = -3.282952598 + 5.666666665
x = -3.282952598 + 5.666666665

Combine like terms: -3.282952598 + 5.666666665 = 2.383714067
x = 2.383714067

Simplifying
x = 2.383714067


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.949619263, 2.383714067}

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