3x^2-60x+200=0

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Solution for 3x^2-60x+200=0 equation: 


Simplifying
3x2 + -60x + 200 = 0

Reorder the terms:
200 + -60x + 3x2 = 0

Solving
200 + -60x + 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'.
66.66666667 + -20x + x2 = 0

Move the constant term to the right:

Add '-66.66666667' to each side of the equation.
66.66666667 + -20x + -66.66666667 + x2 = 0 + -66.66666667

Reorder the terms:
66.66666667 + -66.66666667 + -20x + x2 = 0 + -66.66666667

Combine like terms: 66.66666667 + -66.66666667 = 0.00000000
0.00000000 + -20x + x2 = 0 + -66.66666667
-20x + x2 = 0 + -66.66666667

Combine like terms: 0 + -66.66666667 = -66.66666667
-20x + x2 = -66.66666667

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -66.66666667 + 100

Reorder the terms:
100 + -20x + x2 = -66.66666667 + 100

Combine like terms: -66.66666667 + 100 = 33.33333333
100 + -20x + x2 = 33.33333333

Factor a perfect square on the left side:
(x + -10)(x + -10) = 33.33333333

Calculate the square root of the right side: 5.773502692

Break this problem into two subproblems by setting 
(x + -10) equal to 5.773502692 and -5.773502692.


Subproblem 1
x + -10 = 5.773502692

Simplifying
x + -10 = 5.773502692

Reorder the terms:
-10 + x = 5.773502692

Solving
-10 + x = 5.773502692

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 5.773502692 + 10

Combine like terms: -10 + 10 = 0
0 + x = 5.773502692 + 10
x = 5.773502692 + 10

Combine like terms: 5.773502692 + 10 = 15.773502692
x = 15.773502692

Simplifying
x = 15.773502692


Subproblem 2
x + -10 = -5.773502692

Simplifying
x + -10 = -5.773502692

Reorder the terms:
-10 + x = -5.773502692

Solving
-10 + x = -5.773502692

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -5.773502692 + 10

Combine like terms: -10 + 10 = 0
0 + x = -5.773502692 + 10
x = -5.773502692 + 10

Combine like terms: -5.773502692 + 10 = 4.226497308
x = 4.226497308

Simplifying
x = 4.226497308


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.773502692, 4.226497308}

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