200=3x^2-50x+30

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Solution for 200=3x^2-50x+30 equation:


Simplifying
200 = 3x2 + -50x + 30

Reorder the terms:
200 = 30 + -50x + 3x2

Solving
200 = 30 + -50x + 3x2

Solving for variable 'x'.

Combine like terms: 200 + -30 = 170
170 + 50x + -3x2 = 30 + -50x + 3x2 + -30 + 50x + -3x2

Reorder the terms:
170 + 50x + -3x2 = 30 + -30 + -50x + 50x + 3x2 + -3x2

Combine like terms: 30 + -30 = 0
170 + 50x + -3x2 = 0 + -50x + 50x + 3x2 + -3x2
170 + 50x + -3x2 = -50x + 50x + 3x2 + -3x2

Combine like terms: -50x + 50x = 0
170 + 50x + -3x2 = 0 + 3x2 + -3x2
170 + 50x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
170 + 50x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-56.66666667 + -16.66666667x + x2 = 0

Move the constant term to the right:

Add '56.66666667' to each side of the equation.
-56.66666667 + -16.66666667x + 56.66666667 + x2 = 0 + 56.66666667

Reorder the terms:
-56.66666667 + 56.66666667 + -16.66666667x + x2 = 0 + 56.66666667

Combine like terms: -56.66666667 + 56.66666667 = 0.00000000
0.00000000 + -16.66666667x + x2 = 0 + 56.66666667
-16.66666667x + x2 = 0 + 56.66666667

Combine like terms: 0 + 56.66666667 = 56.66666667
-16.66666667x + x2 = 56.66666667

The x term is -16.66666667x.  Take half its coefficient (-8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
-16.66666667x + 69.44444447 + x2 = 56.66666667 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667x + x2 = 56.66666667 + 69.44444447

Combine like terms: 56.66666667 + 69.44444447 = 126.11111114
69.44444447 + -16.66666667x + x2 = 126.11111114

Factor a perfect square on the left side:
(x + -8.333333335)(x + -8.333333335) = 126.11111114

Calculate the square root of the right side: 11.229920353

Break this problem into two subproblems by setting 
(x + -8.333333335) equal to 11.229920353 and -11.229920353.

Subproblem 1

x + -8.333333335 = 11.229920353 Simplifying x + -8.333333335 = 11.229920353 Reorder the terms: -8.333333335 + x = 11.229920353 Solving -8.333333335 + x = 11.229920353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = 11.229920353 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 11.229920353 + 8.333333335 x = 11.229920353 + 8.333333335 Combine like terms: 11.229920353 + 8.333333335 = 19.563253688 x = 19.563253688 Simplifying x = 19.563253688

Subproblem 2

x + -8.333333335 = -11.229920353 Simplifying x + -8.333333335 = -11.229920353 Reorder the terms: -8.333333335 + x = -11.229920353 Solving -8.333333335 + x = -11.229920353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = -11.229920353 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -11.229920353 + 8.333333335 x = -11.229920353 + 8.333333335 Combine like terms: -11.229920353 + 8.333333335 = -2.896587018 x = -2.896587018 Simplifying x = -2.896587018

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.563253688, -2.896587018}

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