3x^2-60x+175=0

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Solution for 3x^2-60x+175=0 equation: 


Simplifying
3x2 + -60x + 175 = 0

Reorder the terms:
175 + -60x + 3x2 = 0

Solving
175 + -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'.
58.33333333 + -20x + x2 = 0

Move the constant term to the right:

Add '-58.33333333' to each side of the equation.
58.33333333 + -20x + -58.33333333 + x2 = 0 + -58.33333333

Reorder the terms:
58.33333333 + -58.33333333 + -20x + x2 = 0 + -58.33333333

Combine like terms: 58.33333333 + -58.33333333 = 0.00000000
0.00000000 + -20x + x2 = 0 + -58.33333333
-20x + x2 = 0 + -58.33333333

Combine like terms: 0 + -58.33333333 = -58.33333333
-20x + x2 = -58.33333333

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 = -58.33333333 + 100

Reorder the terms:
100 + -20x + x2 = -58.33333333 + 100

Combine like terms: -58.33333333 + 100 = 41.66666667
100 + -20x + x2 = 41.66666667

Factor a perfect square on the left side:
(x + -10)(x + -10) = 41.66666667

Calculate the square root of the right side: 6.454972244

Break this problem into two subproblems by setting 
(x + -10) equal to 6.454972244 and -6.454972244.


Subproblem 1
x + -10 = 6.454972244

Simplifying
x + -10 = 6.454972244

Reorder the terms:
-10 + x = 6.454972244

Solving
-10 + x = 6.454972244

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 = 6.454972244 + 10

Combine like terms: -10 + 10 = 0
0 + x = 6.454972244 + 10
x = 6.454972244 + 10

Combine like terms: 6.454972244 + 10 = 16.454972244
x = 16.454972244

Simplifying
x = 16.454972244


Subproblem 2
x + -10 = -6.454972244

Simplifying
x + -10 = -6.454972244

Reorder the terms:
-10 + x = -6.454972244

Solving
-10 + x = -6.454972244

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 = -6.454972244 + 10

Combine like terms: -10 + 10 = 0
0 + x = -6.454972244 + 10
x = -6.454972244 + 10

Combine like terms: -6.454972244 + 10 = 3.545027756
x = 3.545027756

Simplifying
x = 3.545027756


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.454972244, 3.545027756}

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