3x^2-34x+92=0

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Solution for 3x^2-34x+92=0 equation: 


Simplifying
3x2 + -34x + 92 = 0

Reorder the terms:
92 + -34x + 3x2 = 0

Solving
92 + -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'.
30.66666667 + -11.33333333x + x2 = 0

Move the constant term to the right:

Add '-30.66666667' to each side of the equation.
30.66666667 + -11.33333333x + -30.66666667 + x2 = 0 + -30.66666667

Reorder the terms:
30.66666667 + -30.66666667 + -11.33333333x + x2 = 0 + -30.66666667

Combine like terms: 30.66666667 + -30.66666667 = 0.00000000
0.00000000 + -11.33333333x + x2 = 0 + -30.66666667
-11.33333333x + x2 = 0 + -30.66666667

Combine like terms: 0 + -30.66666667 = -30.66666667
-11.33333333x + x2 = -30.66666667

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 = -30.66666667 + 32.11111109

Reorder the terms:
32.11111109 + -11.33333333x + x2 = -30.66666667 + 32.11111109

Combine like terms: -30.66666667 + 32.11111109 = 1.44444442
32.11111109 + -11.33333333x + x2 = 1.44444442

Factor a perfect square on the left side:
(x + -5.666666665)(x + -5.666666665) = 1.44444442

Calculate the square root of the right side: 1.201850415

Break this problem into two subproblems by setting 
(x + -5.666666665) equal to 1.201850415 and -1.201850415.


Subproblem 1
x + -5.666666665 = 1.201850415

Simplifying
x + -5.666666665 = 1.201850415

Reorder the terms:
-5.666666665 + x = 1.201850415

Solving
-5.666666665 + x = 1.201850415

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 = 1.201850415 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = 1.201850415 + 5.666666665
x = 1.201850415 + 5.666666665

Combine like terms: 1.201850415 + 5.666666665 = 6.86851708
x = 6.86851708

Simplifying
x = 6.86851708


Subproblem 2
x + -5.666666665 = -1.201850415

Simplifying
x + -5.666666665 = -1.201850415

Reorder the terms:
-5.666666665 + x = -1.201850415

Solving
-5.666666665 + x = -1.201850415

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 = -1.201850415 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = -1.201850415 + 5.666666665
x = -1.201850415 + 5.666666665

Combine like terms: -1.201850415 + 5.666666665 = 4.46481625
x = 4.46481625

Simplifying
x = 4.46481625


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.86851708, 4.46481625}

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