3x^2-52x+168=0

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Solution for 3x^2-52x+168=0 equation: 


Simplifying
3x2 + -52x + 168 = 0

Reorder the terms:
168 + -52x + 3x2 = 0

Solving
168 + -52x + 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'.
56 + -17.33333333x + x2 = 0

Move the constant term to the right:

Add '-56' to each side of the equation.
56 + -17.33333333x + -56 + x2 = 0 + -56

Reorder the terms:
56 + -56 + -17.33333333x + x2 = 0 + -56

Combine like terms: 56 + -56 = 0
0 + -17.33333333x + x2 = 0 + -56
-17.33333333x + x2 = 0 + -56

Combine like terms: 0 + -56 = -56
-17.33333333x + x2 = -56

The x term is -17.33333333x.  Take half its coefficient (-8.666666665).
Square it (75.11111108) and add it to both sides.

Add '75.11111108' to each side of the equation.
-17.33333333x + 75.11111108 + x2 = -56 + 75.11111108

Reorder the terms:
75.11111108 + -17.33333333x + x2 = -56 + 75.11111108

Combine like terms: -56 + 75.11111108 = 19.11111108
75.11111108 + -17.33333333x + x2 = 19.11111108

Factor a perfect square on the left side:
(x + -8.666666665)(x + -8.666666665) = 19.11111108

Calculate the square root of the right side: 4.371625679

Break this problem into two subproblems by setting 
(x + -8.666666665) equal to 4.371625679 and -4.371625679.


Subproblem 1
x + -8.666666665 = 4.371625679

Simplifying
x + -8.666666665 = 4.371625679

Reorder the terms:
-8.666666665 + x = 4.371625679

Solving
-8.666666665 + x = 4.371625679

Solving for variable 'x'.

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

Add '8.666666665' to each side of the equation.
-8.666666665 + 8.666666665 + x = 4.371625679 + 8.666666665

Combine like terms: -8.666666665 + 8.666666665 = 0.000000000
0.000000000 + x = 4.371625679 + 8.666666665
x = 4.371625679 + 8.666666665

Combine like terms: 4.371625679 + 8.666666665 = 13.038292344
x = 13.038292344

Simplifying
x = 13.038292344


Subproblem 2
x + -8.666666665 = -4.371625679

Simplifying
x + -8.666666665 = -4.371625679

Reorder the terms:
-8.666666665 + x = -4.371625679

Solving
-8.666666665 + x = -4.371625679

Solving for variable 'x'.

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

Add '8.666666665' to each side of the equation.
-8.666666665 + 8.666666665 + x = -4.371625679 + 8.666666665

Combine like terms: -8.666666665 + 8.666666665 = 0.000000000
0.000000000 + x = -4.371625679 + 8.666666665
x = -4.371625679 + 8.666666665

Combine like terms: -4.371625679 + 8.666666665 = 4.295040986
x = 4.295040986

Simplifying
x = 4.295040986


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.038292344, 4.295040986}

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