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Simplifying 10000 = -0.15x2 + 150x + -2150 Reorder the terms: 10000 = -2150 + 150x + -0.15x2 Solving 10000 = -2150 + 150x + -0.15x2 Solving for variable 'x'. Combine like terms: 10000 + 2150 = 12150 12150 + -150x + 0.15x2 = -2150 + 150x + -0.15x2 + 2150 + -150x + 0.15x2 Reorder the terms: 12150 + -150x + 0.15x2 = -2150 + 2150 + 150x + -150x + -0.15x2 + 0.15x2 Combine like terms: -2150 + 2150 = 0 12150 + -150x + 0.15x2 = 0 + 150x + -150x + -0.15x2 + 0.15x2 12150 + -150x + 0.15x2 = 150x + -150x + -0.15x2 + 0.15x2 Combine like terms: 150x + -150x = 0 12150 + -150x + 0.15x2 = 0 + -0.15x2 + 0.15x2 12150 + -150x + 0.15x2 = -0.15x2 + 0.15x2 Combine like terms: -0.15x2 + 0.15x2 = 0.00 12150 + -150x + 0.15x2 = 0.00 Begin completing the square. Divide all terms by 0.15 the coefficient of the squared term: Divide each side by '0.15'. 81000 + -1000x + x2 = 0 Move the constant term to the right: Add '-81000' to each side of the equation. 81000 + -1000x + -81000 + x2 = 0 + -81000 Reorder the terms: 81000 + -81000 + -1000x + x2 = 0 + -81000 Combine like terms: 81000 + -81000 = 0 0 + -1000x + x2 = 0 + -81000 -1000x + x2 = 0 + -81000 Combine like terms: 0 + -81000 = -81000 -1000x + x2 = -81000 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 = -81000 + 250000 Reorder the terms: 250000 + -1000x + x2 = -81000 + 250000 Combine like terms: -81000 + 250000 = 169000 250000 + -1000x + x2 = 169000 Factor a perfect square on the left side: (x + -500)(x + -500) = 169000 Calculate the square root of the right side: 411.096095822 Break this problem into two subproblems by setting (x + -500) equal to 411.096095822 and -411.096095822.Subproblem 1
x + -500 = 411.096095822 Simplifying x + -500 = 411.096095822 Reorder the terms: -500 + x = 411.096095822 Solving -500 + x = 411.096095822 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 = 411.096095822 + 500 Combine like terms: -500 + 500 = 0 0 + x = 411.096095822 + 500 x = 411.096095822 + 500 Combine like terms: 411.096095822 + 500 = 911.096095822 x = 911.096095822 Simplifying x = 911.096095822Subproblem 2
x + -500 = -411.096095822 Simplifying x + -500 = -411.096095822 Reorder the terms: -500 + x = -411.096095822 Solving -500 + x = -411.096095822 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 = -411.096095822 + 500 Combine like terms: -500 + 500 = 0 0 + x = -411.096095822 + 500 x = -411.096095822 + 500 Combine like terms: -411.096095822 + 500 = 88.903904178 x = 88.903904178 Simplifying x = 88.903904178Solution
The solution to the problem is based on the solutions from the subproblems. x = {911.096095822, 88.903904178}
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