3x^2-34x+54=0

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Solution for 3x^2-34x+54=0 equation: 


Simplifying
3x2 + -34x + 54 = 0

Reorder the terms:
54 + -34x + 3x2 = 0

Solving
54 + -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'.
18 + -11.33333333x + x2 = 0

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -11.33333333x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -11.33333333x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -11.33333333x + x2 = 0 + -18
-11.33333333x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-11.33333333x + x2 = -18

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 = -18 + 32.11111109

Reorder the terms:
32.11111109 + -11.33333333x + x2 = -18 + 32.11111109

Combine like terms: -18 + 32.11111109 = 14.11111109
32.11111109 + -11.33333333x + x2 = 14.11111109

Factor a perfect square on the left side:
(x + -5.666666665)(x + -5.666666665) = 14.11111109

Calculate the square root of the right side: 3.756475887

Break this problem into two subproblems by setting 
(x + -5.666666665) equal to 3.756475887 and -3.756475887.


Subproblem 1
x + -5.666666665 = 3.756475887

Simplifying
x + -5.666666665 = 3.756475887

Reorder the terms:
-5.666666665 + x = 3.756475887

Solving
-5.666666665 + x = 3.756475887

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 = 3.756475887 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = 3.756475887 + 5.666666665
x = 3.756475887 + 5.666666665

Combine like terms: 3.756475887 + 5.666666665 = 9.423142552
x = 9.423142552

Simplifying
x = 9.423142552


Subproblem 2
x + -5.666666665 = -3.756475887

Simplifying
x + -5.666666665 = -3.756475887

Reorder the terms:
-5.666666665 + x = -3.756475887

Solving
-5.666666665 + x = -3.756475887

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 = -3.756475887 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = -3.756475887 + 5.666666665
x = -3.756475887 + 5.666666665

Combine like terms: -3.756475887 + 5.666666665 = 1.910190778
x = 1.910190778

Simplifying
x = 1.910190778


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.423142552, 1.910190778}

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