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Simplifying 11000 = -0.15x2 + 150x Reorder the terms: 11000 = 150x + -0.15x2 Solving 11000 = 150x + -0.15x2 Solving for variable 'x'. Reorder the terms: 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 = 920.317340435 x = 920.317340435 Simplifying x = 920.317340435Subproblem 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 = 79.682659565 x = 79.682659565 Simplifying x = 79.682659565Solution
The solution to the problem is based on the solutions from the subproblems. x = {920.317340435, 79.682659565}
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