3x^2-52x+102=0

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Solution for 3x^2-52x+102=0 equation: 


Simplifying
3x2 + -52x + 102 = 0

Reorder the terms:
102 + -52x + 3x2 = 0

Solving
102 + -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'.
34 + -17.33333333x + x2 = 0

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + -17.33333333x + -34 + x2 = 0 + -34

Reorder the terms:
34 + -34 + -17.33333333x + x2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -17.33333333x + x2 = 0 + -34
-17.33333333x + x2 = 0 + -34

Combine like terms: 0 + -34 = -34
-17.33333333x + x2 = -34

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 = -34 + 75.11111108

Reorder the terms:
75.11111108 + -17.33333333x + x2 = -34 + 75.11111108

Combine like terms: -34 + 75.11111108 = 41.11111108
75.11111108 + -17.33333333x + x2 = 41.11111108

Factor a perfect square on the left side:
(x + -8.666666665)(x + -8.666666665) = 41.11111108

Calculate the square root of the right side: 6.411794685

Break this problem into two subproblems by setting 
(x + -8.666666665) equal to 6.411794685 and -6.411794685.


Subproblem 1
x + -8.666666665 = 6.411794685

Simplifying
x + -8.666666665 = 6.411794685

Reorder the terms:
-8.666666665 + x = 6.411794685

Solving
-8.666666665 + x = 6.411794685

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 = 6.411794685 + 8.666666665

Combine like terms: -8.666666665 + 8.666666665 = 0.000000000
0.000000000 + x = 6.411794685 + 8.666666665
x = 6.411794685 + 8.666666665

Combine like terms: 6.411794685 + 8.666666665 = 15.07846135
x = 15.07846135

Simplifying
x = 15.07846135


Subproblem 2
x + -8.666666665 = -6.411794685

Simplifying
x + -8.666666665 = -6.411794685

Reorder the terms:
-8.666666665 + x = -6.411794685

Solving
-8.666666665 + x = -6.411794685

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 = -6.411794685 + 8.666666665

Combine like terms: -8.666666665 + 8.666666665 = 0.000000000
0.000000000 + x = -6.411794685 + 8.666666665
x = -6.411794685 + 8.666666665

Combine like terms: -6.411794685 + 8.666666665 = 2.25487198
x = 2.25487198

Simplifying
x = 2.25487198


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.07846135, 2.25487198}

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