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Simplifying 10000 = -0.15x2 + -150x + -1000 Reorder the terms: 10000 = -1000 + -150x + -0.15x2 Solving 10000 = -1000 + -150x + -0.15x2 Solving for variable 'x'. Combine like terms: 10000 + 1000 = 11000 11000 + 150x + 0.15x2 = -1000 + -150x + -0.15x2 + 1000 + 150x + 0.15x2 Reorder the terms: 11000 + 150x + 0.15x2 = -1000 + 1000 + -150x + 150x + -0.15x2 + 0.15x2 Combine like terms: -1000 + 1000 = 0 11000 + 150x + 0.15x2 = 0 + -150x + 150x + -0.15x2 + 0.15x2 11000 + 150x + 0.15x2 = -150x + 150x + -0.15x2 + 0.15x2 Combine like terms: -150x + 150x = 0 11000 + 150x + 0.15x2 = 0 + -0.15x2 + 0.15x2 11000 + 150x + 0.15x2 = -0.15x2 + 0.15x2 Combine like terms: -0.15x2 + 0.15x2 = 0.00 11000 + 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'. 73333.33333 + 1000x + x2 = 0 Move the constant term to the right: Add '-73333.33333' to each side of the equation. 73333.33333 + 1000x + -73333.33333 + x2 = 0 + -73333.33333 Reorder the terms: 73333.33333 + -73333.33333 + 1000x + x2 = 0 + -73333.33333 Combine like terms: 73333.33333 + -73333.33333 = 0.00000 0.00000 + 1000x + x2 = 0 + -73333.33333 1000x + x2 = 0 + -73333.33333 Combine like terms: 0 + -73333.33333 = -73333.33333 1000x + x2 = -73333.33333 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 = -73333.33333 + 250000 Reorder the terms: 250000 + 1000x + x2 = -73333.33333 + 250000 Combine like terms: -73333.33333 + 250000 = 176666.66667 250000 + 1000x + x2 = 176666.66667 Factor a perfect square on the left side: (x + 500)(x + 500) = 176666.66667 Calculate the square root of the right side: 420.317340435 Break this problem into two subproblems by setting (x + 500) equal to 420.317340435 and -420.317340435.Subproblem 1
x + 500 = 420.317340435 Simplifying x + 500 = 420.317340435 Reorder the terms: 500 + x = 420.317340435 Solving 500 + x = 420.317340435 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 = 420.317340435 + -500 Combine like terms: 500 + -500 = 0 0 + x = 420.317340435 + -500 x = 420.317340435 + -500 Combine like terms: 420.317340435 + -500 = -79.682659565 x = -79.682659565 Simplifying x = -79.682659565Subproblem 2
x + 500 = -420.317340435 Simplifying x + 500 = -420.317340435 Reorder the terms: 500 + x = -420.317340435 Solving 500 + x = -420.317340435 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 = -420.317340435 + -500 Combine like terms: 500 + -500 = 0 0 + x = -420.317340435 + -500 x = -420.317340435 + -500 Combine like terms: -420.317340435 + -500 = -920.317340435 x = -920.317340435 Simplifying x = -920.317340435Solution
The solution to the problem is based on the solutions from the subproblems. x = {-79.682659565, -920.317340435}
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