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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 = 7850 7850 + -150x + 0.15x2 = 2150 + 150x + -0.15x2 + -2150 + -150x + 0.15x2 Reorder the terms: 7850 + -150x + 0.15x2 = 2150 + -2150 + 150x + -150x + -0.15x2 + 0.15x2 Combine like terms: 2150 + -2150 = 0 7850 + -150x + 0.15x2 = 0 + 150x + -150x + -0.15x2 + 0.15x2 7850 + -150x + 0.15x2 = 150x + -150x + -0.15x2 + 0.15x2 Combine like terms: 150x + -150x = 0 7850 + -150x + 0.15x2 = 0 + -0.15x2 + 0.15x2 7850 + -150x + 0.15x2 = -0.15x2 + 0.15x2 Combine like terms: -0.15x2 + 0.15x2 = 0.00 7850 + -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'. 52333.33333 + -1000x + x2 = 0 Move the constant term to the right: Add '-52333.33333' to each side of the equation. 52333.33333 + -1000x + -52333.33333 + x2 = 0 + -52333.33333 Reorder the terms: 52333.33333 + -52333.33333 + -1000x + x2 = 0 + -52333.33333 Combine like terms: 52333.33333 + -52333.33333 = 0.00000 0.00000 + -1000x + x2 = 0 + -52333.33333 -1000x + x2 = 0 + -52333.33333 Combine like terms: 0 + -52333.33333 = -52333.33333 -1000x + x2 = -52333.33333 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 = -52333.33333 + 250000 Reorder the terms: 250000 + -1000x + x2 = -52333.33333 + 250000 Combine like terms: -52333.33333 + 250000 = 197666.66667 250000 + -1000x + x2 = 197666.66667 Factor a perfect square on the left side: (x + -500)(x + -500) = 197666.66667 Calculate the square root of the right side: 444.597195976 Break this problem into two subproblems by setting (x + -500) equal to 444.597195976 and -444.597195976.Subproblem 1
x + -500 = 444.597195976 Simplifying x + -500 = 444.597195976 Reorder the terms: -500 + x = 444.597195976 Solving -500 + x = 444.597195976 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 = 444.597195976 + 500 Combine like terms: -500 + 500 = 0 0 + x = 444.597195976 + 500 x = 444.597195976 + 500 Combine like terms: 444.597195976 + 500 = 944.597195976 x = 944.597195976 Simplifying x = 944.597195976Subproblem 2
x + -500 = -444.597195976 Simplifying x + -500 = -444.597195976 Reorder the terms: -500 + x = -444.597195976 Solving -500 + x = -444.597195976 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 = -444.597195976 + 500 Combine like terms: -500 + 500 = 0 0 + x = -444.597195976 + 500 x = -444.597195976 + 500 Combine like terms: -444.597195976 + 500 = 55.402804024 x = 55.402804024 Simplifying x = 55.402804024Solution
The solution to the problem is based on the solutions from the subproblems. x = {944.597195976, 55.402804024}
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