3x^2-28x+51=0

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Solution for 3x^2-28x+51=0 equation: 


Simplifying
3x2 + -28x + 51 = 0

Reorder the terms:
51 + -28x + 3x2 = 0

Solving
51 + -28x + 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'.
17 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -9.333333333x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + -9.333333333x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -9.333333333x + x2 = 0 + -17
-9.333333333x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
-9.333333333x + x2 = -17

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = -17 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = -17 + 21.77777778

Combine like terms: -17 + 21.77777778 = 4.77777778
21.77777778 + -9.333333333x + x2 = 4.77777778

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 4.77777778

Calculate the square root of the right side: 2.185812842

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 2.185812842 and -2.185812842.


Subproblem 1
x + -4.666666667 = 2.185812842

Simplifying
x + -4.666666667 = 2.185812842

Reorder the terms:
-4.666666667 + x = 2.185812842

Solving
-4.666666667 + x = 2.185812842

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = 2.185812842 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = 2.185812842 + 4.666666667
x = 2.185812842 + 4.666666667

Combine like terms: 2.185812842 + 4.666666667 = 6.852479509
x = 6.852479509

Simplifying
x = 6.852479509


Subproblem 2
x + -4.666666667 = -2.185812842

Simplifying
x + -4.666666667 = -2.185812842

Reorder the terms:
-4.666666667 + x = -2.185812842

Solving
-4.666666667 + x = -2.185812842

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = -2.185812842 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = -2.185812842 + 4.666666667
x = -2.185812842 + 4.666666667

Combine like terms: -2.185812842 + 4.666666667 = 2.480853825
x = 2.480853825

Simplifying
x = 2.480853825


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.852479509, 2.480853825}

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