3x^2-100x+650=0

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Solution for 3x^2-100x+650=0 equation: 


Simplifying
3x2 + -100x + 650 = 0

Reorder the terms:
650 + -100x + 3x2 = 0

Solving
650 + -100x + 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'.
216.6666667 + -33.33333333x + x2 = 0

Move the constant term to the right:

Add '-216.6666667' to each side of the equation.
216.6666667 + -33.33333333x + -216.6666667 + x2 = 0 + -216.6666667

Reorder the terms:
216.6666667 + -216.6666667 + -33.33333333x + x2 = 0 + -216.6666667

Combine like terms: 216.6666667 + -216.6666667 = 0.0000000
0.0000000 + -33.33333333x + x2 = 0 + -216.6666667
-33.33333333x + x2 = 0 + -216.6666667

Combine like terms: 0 + -216.6666667 = -216.6666667
-33.33333333x + x2 = -216.6666667

The x term is -33.33333333x.  Take half its coefficient (-16.66666667).
Square it (277.7777779) and add it to both sides.

Add '277.7777779' to each side of the equation.
-33.33333333x + 277.7777779 + x2 = -216.6666667 + 277.7777779

Reorder the terms:
277.7777779 + -33.33333333x + x2 = -216.6666667 + 277.7777779

Combine like terms: -216.6666667 + 277.7777779 = 61.1111112
277.7777779 + -33.33333333x + x2 = 61.1111112

Factor a perfect square on the left side:
(x + -16.66666667)(x + -16.66666667) = 61.1111112

Calculate the square root of the right side: 7.817359605

Break this problem into two subproblems by setting 
(x + -16.66666667) equal to 7.817359605 and -7.817359605.


Subproblem 1
x + -16.66666667 = 7.817359605

Simplifying
x + -16.66666667 = 7.817359605

Reorder the terms:
-16.66666667 + x = 7.817359605

Solving
-16.66666667 + x = 7.817359605

Solving for variable 'x'.

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

Add '16.66666667' to each side of the equation.
-16.66666667 + 16.66666667 + x = 7.817359605 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + x = 7.817359605 + 16.66666667
x = 7.817359605 + 16.66666667

Combine like terms: 7.817359605 + 16.66666667 = 24.484026275
x = 24.484026275

Simplifying
x = 24.484026275


Subproblem 2
x + -16.66666667 = -7.817359605

Simplifying
x + -16.66666667 = -7.817359605

Reorder the terms:
-16.66666667 + x = -7.817359605

Solving
-16.66666667 + x = -7.817359605

Solving for variable 'x'.

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

Add '16.66666667' to each side of the equation.
-16.66666667 + 16.66666667 + x = -7.817359605 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + x = -7.817359605 + 16.66666667
x = -7.817359605 + 16.66666667

Combine like terms: -7.817359605 + 16.66666667 = 8.849307065
x = 8.849307065

Simplifying
x = 8.849307065


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.484026275, 8.849307065}

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