3x^2-60x+50=0

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Solution for 3x^2-60x+50=0 equation:


Simplifying
3x2 + -60x + 50 = 0

Reorder the terms:
50 + -60x + 3x2 = 0

Solving
50 + -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'.
16.66666667 + -20x + x2 = 0

Move the constant term to the right:

Add '-16.66666667' to each side of the equation.
16.66666667 + -20x + -16.66666667 + x2 = 0 + -16.66666667

Reorder the terms:
16.66666667 + -16.66666667 + -20x + x2 = 0 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + -20x + x2 = 0 + -16.66666667
-20x + x2 = 0 + -16.66666667

Combine like terms: 0 + -16.66666667 = -16.66666667
-20x + x2 = -16.66666667

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 = -16.66666667 + 100

Reorder the terms:
100 + -20x + x2 = -16.66666667 + 100

Combine like terms: -16.66666667 + 100 = 83.33333333
100 + -20x + x2 = 83.33333333

Factor a perfect square on the left side:
(x + -10)(x + -10) = 83.33333333

Calculate the square root of the right side: 9.128709292

Break this problem into two subproblems by setting 
(x + -10) equal to 9.128709292 and -9.128709292.

Subproblem 1

x + -10 = 9.128709292 Simplifying x + -10 = 9.128709292 Reorder the terms: -10 + x = 9.128709292 Solving -10 + x = 9.128709292 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 = 9.128709292 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.128709292 + 10 x = 9.128709292 + 10 Combine like terms: 9.128709292 + 10 = 19.128709292 x = 19.128709292 Simplifying x = 19.128709292

Subproblem 2

x + -10 = -9.128709292 Simplifying x + -10 = -9.128709292 Reorder the terms: -10 + x = -9.128709292 Solving -10 + x = -9.128709292 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 = -9.128709292 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.128709292 + 10 x = -9.128709292 + 10 Combine like terms: -9.128709292 + 10 = 0.871290708 x = 0.871290708 Simplifying x = 0.871290708

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.128709292, 0.871290708}

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