3x^2-50x+150=0

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Solution for 3x^2-50x+150=0 equation: 


Simplifying
3x2 + -50x + 150 = 0

Reorder the terms:
150 + -50x + 3x2 = 0

Solving
150 + -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'.
50 + -16.66666667x + x2 = 0

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -16.66666667x + -50 + x2 = 0 + -50

Reorder the terms:
50 + -50 + -16.66666667x + x2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -16.66666667x + x2 = 0 + -50
-16.66666667x + x2 = 0 + -50

Combine like terms: 0 + -50 = -50
-16.66666667x + x2 = -50

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 = -50 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667x + x2 = -50 + 69.44444447

Combine like terms: -50 + 69.44444447 = 19.44444447
69.44444447 + -16.66666667x + x2 = 19.44444447

Factor a perfect square on the left side:
(x + -8.333333335)(x + -8.333333335) = 19.44444447

Calculate the square root of the right side: 4.409585521

Break this problem into two subproblems by setting 
(x + -8.333333335) equal to 4.409585521 and -4.409585521.


Subproblem 1
x + -8.333333335 = 4.409585521

Simplifying
x + -8.333333335 = 4.409585521

Reorder the terms:
-8.333333335 + x = 4.409585521

Solving
-8.333333335 + x = 4.409585521

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 = 4.409585521 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = 4.409585521 + 8.333333335
x = 4.409585521 + 8.333333335

Combine like terms: 4.409585521 + 8.333333335 = 12.742918856
x = 12.742918856

Simplifying
x = 12.742918856


Subproblem 2
x + -8.333333335 = -4.409585521

Simplifying
x + -8.333333335 = -4.409585521

Reorder the terms:
-8.333333335 + x = -4.409585521

Solving
-8.333333335 + x = -4.409585521

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 = -4.409585521 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = -4.409585521 + 8.333333335
x = -4.409585521 + 8.333333335

Combine like terms: -4.409585521 + 8.333333335 = 3.923747814
x = 3.923747814

Simplifying
x = 3.923747814


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.742918856, 3.923747814}

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