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Simplifying -0.2x2 + 100x + -9500 = 0 Reorder the terms: -9500 + 100x + -0.2x2 = 0 Solving -9500 + 100x + -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 + -500x + x2 = 0 Move the constant term to the right: Add '-47500' to each side of the equation. 47500 + -500x + -47500 + x2 = 0 + -47500 Reorder the terms: 47500 + -47500 + -500x + x2 = 0 + -47500 Combine like terms: 47500 + -47500 = 0 0 + -500x + x2 = 0 + -47500 -500x + x2 = 0 + -47500 Combine like terms: 0 + -47500 = -47500 -500x + x2 = -47500 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = -47500 + 62500 Reorder the terms: 62500 + -500x + x2 = -47500 + 62500 Combine like terms: -47500 + 62500 = 15000 62500 + -500x + x2 = 15000 Factor a perfect square on the left side: (x + -250)(x + -250) = 15000 Calculate the square root of the right side: 122.474487139 Break this problem into two subproblems by setting (x + -250) equal to 122.474487139 and -122.474487139.Subproblem 1
x + -250 = 122.474487139 Simplifying x + -250 = 122.474487139 Reorder the terms: -250 + x = 122.474487139 Solving -250 + x = 122.474487139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 122.474487139 + 250 Combine like terms: -250 + 250 = 0 0 + x = 122.474487139 + 250 x = 122.474487139 + 250 Combine like terms: 122.474487139 + 250 = 372.474487139 x = 372.474487139 Simplifying x = 372.474487139Subproblem 2
x + -250 = -122.474487139 Simplifying x + -250 = -122.474487139 Reorder the terms: -250 + x = -122.474487139 Solving -250 + x = -122.474487139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -122.474487139 + 250 Combine like terms: -250 + 250 = 0 0 + x = -122.474487139 + 250 x = -122.474487139 + 250 Combine like terms: -122.474487139 + 250 = 127.525512861 x = 127.525512861 Simplifying x = 127.525512861Solution
The solution to the problem is based on the solutions from the subproblems. x = {372.474487139, 127.525512861}
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