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Simplifying 100 = 10000 + 150x + -0.2x2 Solving 100 = 10000 + 150x + -0.2x2 Solving for variable 'x'. Combine like terms: 100 + -10000 = -9900 -9900 + -150x + 0.2x2 = 10000 + 150x + -0.2x2 + -10000 + -150x + 0.2x2 Reorder the terms: -9900 + -150x + 0.2x2 = 10000 + -10000 + 150x + -150x + -0.2x2 + 0.2x2 Combine like terms: 10000 + -10000 = 0 -9900 + -150x + 0.2x2 = 0 + 150x + -150x + -0.2x2 + 0.2x2 -9900 + -150x + 0.2x2 = 150x + -150x + -0.2x2 + 0.2x2 Combine like terms: 150x + -150x = 0 -9900 + -150x + 0.2x2 = 0 + -0.2x2 + 0.2x2 -9900 + -150x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 -9900 + -150x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -49500 + -750x + x2 = 0 Move the constant term to the right: Add '49500' to each side of the equation. -49500 + -750x + 49500 + x2 = 0 + 49500 Reorder the terms: -49500 + 49500 + -750x + x2 = 0 + 49500 Combine like terms: -49500 + 49500 = 0 0 + -750x + x2 = 0 + 49500 -750x + x2 = 0 + 49500 Combine like terms: 0 + 49500 = 49500 -750x + x2 = 49500 The x term is -750x. Take half its coefficient (-375). Square it (140625) and add it to both sides. Add '140625' to each side of the equation. -750x + 140625 + x2 = 49500 + 140625 Reorder the terms: 140625 + -750x + x2 = 49500 + 140625 Combine like terms: 49500 + 140625 = 190125 140625 + -750x + x2 = 190125 Factor a perfect square on the left side: (x + -375)(x + -375) = 190125 Calculate the square root of the right side: 436.033255612 Break this problem into two subproblems by setting (x + -375) equal to 436.033255612 and -436.033255612.Subproblem 1
x + -375 = 436.033255612 Simplifying x + -375 = 436.033255612 Reorder the terms: -375 + x = 436.033255612 Solving -375 + x = 436.033255612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '375' to each side of the equation. -375 + 375 + x = 436.033255612 + 375 Combine like terms: -375 + 375 = 0 0 + x = 436.033255612 + 375 x = 436.033255612 + 375 Combine like terms: 436.033255612 + 375 = 811.033255612 x = 811.033255612 Simplifying x = 811.033255612Subproblem 2
x + -375 = -436.033255612 Simplifying x + -375 = -436.033255612 Reorder the terms: -375 + x = -436.033255612 Solving -375 + x = -436.033255612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '375' to each side of the equation. -375 + 375 + x = -436.033255612 + 375 Combine like terms: -375 + 375 = 0 0 + x = -436.033255612 + 375 x = -436.033255612 + 375 Combine like terms: -436.033255612 + 375 = -61.033255612 x = -61.033255612 Simplifying x = -61.033255612Solution
The solution to the problem is based on the solutions from the subproblems. x = {811.033255612, -61.033255612}
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