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Simplifying -0.2x2 + 200x + -9500 = 0 Reorder the terms: -9500 + 200x + -0.2x2 = 0 Solving -9500 + 200x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 47500 + -1000x + x2 = 0 Move the constant term to the right: Add '-47500' to each side of the equation. 47500 + -1000x + -47500 + x2 = 0 + -47500 Reorder the terms: 47500 + -47500 + -1000x + x2 = 0 + -47500 Combine like terms: 47500 + -47500 = 0 0 + -1000x + x2 = 0 + -47500 -1000x + x2 = 0 + -47500 Combine like terms: 0 + -47500 = -47500 -1000x + x2 = -47500 The x term is -1000x. Take half its coefficient (-500). Square it (250000) and add it to both sides. Add '250000' to each side of the equation. -1000x + 250000 + x2 = -47500 + 250000 Reorder the terms: 250000 + -1000x + x2 = -47500 + 250000 Combine like terms: -47500 + 250000 = 202500 250000 + -1000x + x2 = 202500 Factor a perfect square on the left side: (x + -500)(x + -500) = 202500 Calculate the square root of the right side: 450 Break this problem into two subproblems by setting (x + -500) equal to 450 and -450.Subproblem 1
x + -500 = 450 Simplifying x + -500 = 450 Reorder the terms: -500 + x = 450 Solving -500 + x = 450 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = 450 + 500 Combine like terms: -500 + 500 = 0 0 + x = 450 + 500 x = 450 + 500 Combine like terms: 450 + 500 = 950 x = 950 Simplifying x = 950Subproblem 2
x + -500 = -450 Simplifying x + -500 = -450 Reorder the terms: -500 + x = -450 Solving -500 + x = -450 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = -450 + 500 Combine like terms: -500 + 500 = 0 0 + x = -450 + 500 x = -450 + 500 Combine like terms: -450 + 500 = 50 x = 50 Simplifying x = 50Solution
The solution to the problem is based on the solutions from the subproblems. x = {950, 50}
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