3x^2-50x+100=0

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Solution for 3x^2-50x+100=0 equation: 


Simplifying
3x2 + -50x + 100 = 0

Reorder the terms:
100 + -50x + 3x2 = 0

Solving
100 + -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'.
33.33333333 + -16.66666667x + x2 = 0

Move the constant term to the right:

Add '-33.33333333' to each side of the equation.
33.33333333 + -16.66666667x + -33.33333333 + x2 = 0 + -33.33333333

Reorder the terms:
33.33333333 + -33.33333333 + -16.66666667x + x2 = 0 + -33.33333333

Combine like terms: 33.33333333 + -33.33333333 = 0.00000000
0.00000000 + -16.66666667x + x2 = 0 + -33.33333333
-16.66666667x + x2 = 0 + -33.33333333

Combine like terms: 0 + -33.33333333 = -33.33333333
-16.66666667x + x2 = -33.33333333

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 = -33.33333333 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667x + x2 = -33.33333333 + 69.44444447

Combine like terms: -33.33333333 + 69.44444447 = 36.11111114
69.44444447 + -16.66666667x + x2 = 36.11111114

Factor a perfect square on the left side:
(x + -8.333333335)(x + -8.333333335) = 36.11111114

Calculate the square root of the right side: 6.009252128

Break this problem into two subproblems by setting 
(x + -8.333333335) equal to 6.009252128 and -6.009252128.


Subproblem 1
x + -8.333333335 = 6.009252128

Simplifying
x + -8.333333335 = 6.009252128

Reorder the terms:
-8.333333335 + x = 6.009252128

Solving
-8.333333335 + x = 6.009252128

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 = 6.009252128 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = 6.009252128 + 8.333333335
x = 6.009252128 + 8.333333335

Combine like terms: 6.009252128 + 8.333333335 = 14.342585463
x = 14.342585463

Simplifying
x = 14.342585463


Subproblem 2
x + -8.333333335 = -6.009252128

Simplifying
x + -8.333333335 = -6.009252128

Reorder the terms:
-8.333333335 + x = -6.009252128

Solving
-8.333333335 + x = -6.009252128

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 = -6.009252128 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = -6.009252128 + 8.333333335
x = -6.009252128 + 8.333333335

Combine like terms: -6.009252128 + 8.333333335 = 2.324081207
x = 2.324081207

Simplifying
x = 2.324081207


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.342585463, 2.324081207}

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