3x^2-50x+101=0

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Solution for 3x^2-50x+101=0 equation: 


Simplifying
3x2 + -50x + 101 = 0

Reorder the terms:
101 + -50x + 3x2 = 0

Solving
101 + -50x + 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'.
33.66666667 + -16.66666667x + x2 = 0

Move the constant term to the right:

Add '-33.66666667' to each side of the equation.
33.66666667 + -16.66666667x + -33.66666667 + x2 = 0 + -33.66666667

Reorder the terms:
33.66666667 + -33.66666667 + -16.66666667x + x2 = 0 + -33.66666667

Combine like terms: 33.66666667 + -33.66666667 = 0.00000000
0.00000000 + -16.66666667x + x2 = 0 + -33.66666667
-16.66666667x + x2 = 0 + -33.66666667

Combine like terms: 0 + -33.66666667 = -33.66666667
-16.66666667x + x2 = -33.66666667

The x term is -16.66666667x.  Take half its coefficient (-8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
-16.66666667x + 69.44444447 + x2 = -33.66666667 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667x + x2 = -33.66666667 + 69.44444447

Combine like terms: -33.66666667 + 69.44444447 = 35.7777778
69.44444447 + -16.66666667x + x2 = 35.7777778

Factor a perfect square on the left side:
(x + -8.333333335)(x + -8.333333335) = 35.7777778

Calculate the square root of the right side: 5.981452817

Break this problem into two subproblems by setting 
(x + -8.333333335) equal to 5.981452817 and -5.981452817.


Subproblem 1
x + -8.333333335 = 5.981452817

Simplifying
x + -8.333333335 = 5.981452817

Reorder the terms:
-8.333333335 + x = 5.981452817

Solving
-8.333333335 + x = 5.981452817

Solving for variable 'x'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + x = 5.981452817 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = 5.981452817 + 8.333333335
x = 5.981452817 + 8.333333335

Combine like terms: 5.981452817 + 8.333333335 = 14.314786152
x = 14.314786152

Simplifying
x = 14.314786152


Subproblem 2
x + -8.333333335 = -5.981452817

Simplifying
x + -8.333333335 = -5.981452817

Reorder the terms:
-8.333333335 + x = -5.981452817

Solving
-8.333333335 + x = -5.981452817

Solving for variable 'x'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + x = -5.981452817 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = -5.981452817 + 8.333333335
x = -5.981452817 + 8.333333335

Combine like terms: -5.981452817 + 8.333333335 = 2.351880518
x = 2.351880518

Simplifying
x = 2.351880518


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.314786152, 2.351880518}

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