3x^2-180x+2000=0

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Solution for 3x^2-180x+2000=0 equation:


Simplifying
3x2 + -180x + 2000 = 0

Reorder the terms:
2000 + -180x + 3x2 = 0

Solving
2000 + -180x + 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'.
666.6666667 + -60x + x2 = 0

Move the constant term to the right:

Add '-666.6666667' to each side of the equation.
666.6666667 + -60x + -666.6666667 + x2 = 0 + -666.6666667

Reorder the terms:
666.6666667 + -666.6666667 + -60x + x2 = 0 + -666.6666667

Combine like terms: 666.6666667 + -666.6666667 = 0.0000000
0.0000000 + -60x + x2 = 0 + -666.6666667
-60x + x2 = 0 + -666.6666667

Combine like terms: 0 + -666.6666667 = -666.6666667
-60x + x2 = -666.6666667

The x term is -60x.  Take half its coefficient (-30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
-60x + 900 + x2 = -666.6666667 + 900

Reorder the terms:
900 + -60x + x2 = -666.6666667 + 900

Combine like terms: -666.6666667 + 900 = 233.3333333
900 + -60x + x2 = 233.3333333

Factor a perfect square on the left side:
(x + -30)(x + -30) = 233.3333333

Calculate the square root of the right side: 15.275252315

Break this problem into two subproblems by setting 
(x + -30) equal to 15.275252315 and -15.275252315.

Subproblem 1

x + -30 = 15.275252315 Simplifying x + -30 = 15.275252315 Reorder the terms: -30 + x = 15.275252315 Solving -30 + x = 15.275252315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 15.275252315 + 30 Combine like terms: -30 + 30 = 0 0 + x = 15.275252315 + 30 x = 15.275252315 + 30 Combine like terms: 15.275252315 + 30 = 45.275252315 x = 45.275252315 Simplifying x = 45.275252315

Subproblem 2

x + -30 = -15.275252315 Simplifying x + -30 = -15.275252315 Reorder the terms: -30 + x = -15.275252315 Solving -30 + x = -15.275252315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -15.275252315 + 30 Combine like terms: -30 + 30 = 0 0 + x = -15.275252315 + 30 x = -15.275252315 + 30 Combine like terms: -15.275252315 + 30 = 14.724747685 x = 14.724747685 Simplifying x = 14.724747685

Solution

The solution to the problem is based on the solutions from the subproblems. x = {45.275252315, 14.724747685}

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