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Simplifying (x) = -0.04x2 + 240x + -10000 x = -0.04x2 + 240x + -10000 Reorder the terms: x = -10000 + 240x + -0.04x2 Solving x = -10000 + 240x + -0.04x2 Solving for variable 'x'. Reorder the terms: 10000 + x + -240x + 0.04x2 = -10000 + 240x + -0.04x2 + 10000 + -240x + 0.04x2 Combine like terms: x + -240x = -239x 10000 + -239x + 0.04x2 = -10000 + 240x + -0.04x2 + 10000 + -240x + 0.04x2 Reorder the terms: 10000 + -239x + 0.04x2 = -10000 + 10000 + 240x + -240x + -0.04x2 + 0.04x2 Combine like terms: -10000 + 10000 = 0 10000 + -239x + 0.04x2 = 0 + 240x + -240x + -0.04x2 + 0.04x2 10000 + -239x + 0.04x2 = 240x + -240x + -0.04x2 + 0.04x2 Combine like terms: 240x + -240x = 0 10000 + -239x + 0.04x2 = 0 + -0.04x2 + 0.04x2 10000 + -239x + 0.04x2 = -0.04x2 + 0.04x2 Combine like terms: -0.04x2 + 0.04x2 = 0.00 10000 + -239x + 0.04x2 = 0.00 Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 250000 + -5975x + x2 = 0 Move the constant term to the right: Add '-250000' to each side of the equation. 250000 + -5975x + -250000 + x2 = 0 + -250000 Reorder the terms: 250000 + -250000 + -5975x + x2 = 0 + -250000 Combine like terms: 250000 + -250000 = 0 0 + -5975x + x2 = 0 + -250000 -5975x + x2 = 0 + -250000 Combine like terms: 0 + -250000 = -250000 -5975x + x2 = -250000 The x term is -5975x. Take half its coefficient (-2987.5). Square it (8925156.25) and add it to both sides. Add '8925156.25' to each side of the equation. -5975x + 8925156.25 + x2 = -250000 + 8925156.25 Reorder the terms: 8925156.25 + -5975x + x2 = -250000 + 8925156.25 Combine like terms: -250000 + 8925156.25 = 8675156.25 8925156.25 + -5975x + x2 = 8675156.25 Factor a perfect square on the left side: (x + -2987.5)(x + -2987.5) = 8675156.25 Calculate the square root of the right side: 2945.361819879 Break this problem into two subproblems by setting (x + -2987.5) equal to 2945.361819879 and -2945.361819879.Subproblem 1
x + -2987.5 = 2945.361819879 Simplifying x + -2987.5 = 2945.361819879 Reorder the terms: -2987.5 + x = 2945.361819879 Solving -2987.5 + x = 2945.361819879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2987.5' to each side of the equation. -2987.5 + 2987.5 + x = 2945.361819879 + 2987.5 Combine like terms: -2987.5 + 2987.5 = 0.0 0.0 + x = 2945.361819879 + 2987.5 x = 2945.361819879 + 2987.5 Combine like terms: 2945.361819879 + 2987.5 = 5932.861819879 x = 5932.861819879 Simplifying x = 5932.861819879Subproblem 2
x + -2987.5 = -2945.361819879 Simplifying x + -2987.5 = -2945.361819879 Reorder the terms: -2987.5 + x = -2945.361819879 Solving -2987.5 + x = -2945.361819879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2987.5' to each side of the equation. -2987.5 + 2987.5 + x = -2945.361819879 + 2987.5 Combine like terms: -2987.5 + 2987.5 = 0.0 0.0 + x = -2945.361819879 + 2987.5 x = -2945.361819879 + 2987.5 Combine like terms: -2945.361819879 + 2987.5 = 42.138180121 x = 42.138180121 Simplifying x = 42.138180121Solution
The solution to the problem is based on the solutions from the subproblems. x = {5932.861819879, 42.138180121}
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