0.2x^2-6x+50=250

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Solution for 0.2x^2-6x+50=250 equation:


Simplifying
0.2x2 + -6x + 50 = 250

Reorder the terms:
50 + -6x + 0.2x2 = 250

Solving
50 + -6x + 0.2x2 = 250

Solving for variable 'x'.

Reorder the terms:
50 + -250 + -6x + 0.2x2 = 250 + -250

Combine like terms: 50 + -250 = -200
-200 + -6x + 0.2x2 = 250 + -250

Combine like terms: 250 + -250 = 0
-200 + -6x + 0.2x2 = 0

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

Divide each side by '0.2'.
-1000 + -30x + x2 = 0

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + -30x + 1000 + x2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + -30x + x2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + -30x + x2 = 0 + 1000
-30x + x2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
-30x + x2 = 1000

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 1000 + 225

Reorder the terms:
225 + -30x + x2 = 1000 + 225

Combine like terms: 1000 + 225 = 1225
225 + -30x + x2 = 1225

Factor a perfect square on the left side:
(x + -15)(x + -15) = 1225

Calculate the square root of the right side: 35

Break this problem into two subproblems by setting 
(x + -15) equal to 35 and -35.

Subproblem 1

x + -15 = 35 Simplifying x + -15 = 35 Reorder the terms: -15 + x = 35 Solving -15 + x = 35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 35 + 15 Combine like terms: -15 + 15 = 0 0 + x = 35 + 15 x = 35 + 15 Combine like terms: 35 + 15 = 50 x = 50 Simplifying x = 50

Subproblem 2

x + -15 = -35 Simplifying x + -15 = -35 Reorder the terms: -15 + x = -35 Solving -15 + x = -35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -35 + 15 Combine like terms: -15 + 15 = 0 0 + x = -35 + 15 x = -35 + 15 Combine like terms: -35 + 15 = -20 x = -20 Simplifying x = -20

Solution

The solution to the problem is based on the solutions from the subproblems. x = {50, -20}

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