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Simplifying 0.20x + 60 = 1.9x + -0.001x2 Reorder the terms: 60 + 0.20x = 1.9x + -0.001x2 Solving 60 + 0.20x = 1.9x + -0.001x2 Solving for variable 'x'. Combine like terms: 0.20x + -1.9x = -1.7x 60 + -1.7x + 0.001x2 = 1.9x + -0.001x2 + -1.9x + 0.001x2 Reorder the terms: 60 + -1.7x + 0.001x2 = 1.9x + -1.9x + -0.001x2 + 0.001x2 Combine like terms: 1.9x + -1.9x = 0.0 60 + -1.7x + 0.001x2 = 0.0 + -0.001x2 + 0.001x2 60 + -1.7x + 0.001x2 = -0.001x2 + 0.001x2 Combine like terms: -0.001x2 + 0.001x2 = 0.000 60 + -1.7x + 0.001x2 = 0.000 Begin completing the square. Divide all terms by 0.001 the coefficient of the squared term: Divide each side by '0.001'. 60000 + -1700x + x2 = 0 Move the constant term to the right: Add '-60000' to each side of the equation. 60000 + -1700x + -60000 + x2 = 0 + -60000 Reorder the terms: 60000 + -60000 + -1700x + x2 = 0 + -60000 Combine like terms: 60000 + -60000 = 0 0 + -1700x + x2 = 0 + -60000 -1700x + x2 = 0 + -60000 Combine like terms: 0 + -60000 = -60000 -1700x + x2 = -60000 The x term is -1700x. Take half its coefficient (-850). Square it (722500) and add it to both sides. Add '722500' to each side of the equation. -1700x + 722500 + x2 = -60000 + 722500 Reorder the terms: 722500 + -1700x + x2 = -60000 + 722500 Combine like terms: -60000 + 722500 = 662500 722500 + -1700x + x2 = 662500 Factor a perfect square on the left side: (x + -850)(x + -850) = 662500 Calculate the square root of the right side: 813.941029805 Break this problem into two subproblems by setting (x + -850) equal to 813.941029805 and -813.941029805.Subproblem 1
x + -850 = 813.941029805 Simplifying x + -850 = 813.941029805 Reorder the terms: -850 + x = 813.941029805 Solving -850 + x = 813.941029805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '850' to each side of the equation. -850 + 850 + x = 813.941029805 + 850 Combine like terms: -850 + 850 = 0 0 + x = 813.941029805 + 850 x = 813.941029805 + 850 Combine like terms: 813.941029805 + 850 = 1663.941029805 x = 1663.941029805 Simplifying x = 1663.941029805Subproblem 2
x + -850 = -813.941029805 Simplifying x + -850 = -813.941029805 Reorder the terms: -850 + x = -813.941029805 Solving -850 + x = -813.941029805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '850' to each side of the equation. -850 + 850 + x = -813.941029805 + 850 Combine like terms: -850 + 850 = 0 0 + x = -813.941029805 + 850 x = -813.941029805 + 850 Combine like terms: -813.941029805 + 850 = 36.058970195 x = 36.058970195 Simplifying x = 36.058970195Solution
The solution to the problem is based on the solutions from the subproblems. x = {1663.941029805, 36.058970195}
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