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Simplifying 1000 = x(12 + -0.025x) 1000 = (12 * x + -0.025x * x) 1000 = (12x + -0.025x2) Solving 1000 = 12x + -0.025x2 Solving for variable 'x'. Reorder the terms: 1000 + -12x + 0.025x2 = 12x + -12x + -0.025x2 + 0.025x2 Combine like terms: 12x + -12x = 0 1000 + -12x + 0.025x2 = 0 + -0.025x2 + 0.025x2 1000 + -12x + 0.025x2 = -0.025x2 + 0.025x2 Combine like terms: -0.025x2 + 0.025x2 = 0.000 1000 + -12x + 0.025x2 = 0.000 Begin completing the square. Divide all terms by 0.025 the coefficient of the squared term: Divide each side by '0.025'. 40000 + -480x + x2 = 0 Move the constant term to the right: Add '-40000' to each side of the equation. 40000 + -480x + -40000 + x2 = 0 + -40000 Reorder the terms: 40000 + -40000 + -480x + x2 = 0 + -40000 Combine like terms: 40000 + -40000 = 0 0 + -480x + x2 = 0 + -40000 -480x + x2 = 0 + -40000 Combine like terms: 0 + -40000 = -40000 -480x + x2 = -40000 The x term is -480x. Take half its coefficient (-240). Square it (57600) and add it to both sides. Add '57600' to each side of the equation. -480x + 57600 + x2 = -40000 + 57600 Reorder the terms: 57600 + -480x + x2 = -40000 + 57600 Combine like terms: -40000 + 57600 = 17600 57600 + -480x + x2 = 17600 Factor a perfect square on the left side: (x + -240)(x + -240) = 17600 Calculate the square root of the right side: 132.664991614 Break this problem into two subproblems by setting (x + -240) equal to 132.664991614 and -132.664991614.Subproblem 1
x + -240 = 132.664991614 Simplifying x + -240 = 132.664991614 Reorder the terms: -240 + x = 132.664991614 Solving -240 + x = 132.664991614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '240' to each side of the equation. -240 + 240 + x = 132.664991614 + 240 Combine like terms: -240 + 240 = 0 0 + x = 132.664991614 + 240 x = 132.664991614 + 240 Combine like terms: 132.664991614 + 240 = 372.664991614 x = 372.664991614 Simplifying x = 372.664991614Subproblem 2
x + -240 = -132.664991614 Simplifying x + -240 = -132.664991614 Reorder the terms: -240 + x = -132.664991614 Solving -240 + x = -132.664991614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '240' to each side of the equation. -240 + 240 + x = -132.664991614 + 240 Combine like terms: -240 + 240 = 0 0 + x = -132.664991614 + 240 x = -132.664991614 + 240 Combine like terms: -132.664991614 + 240 = 107.335008386 x = 107.335008386 Simplifying x = 107.335008386Solution
The solution to the problem is based on the solutions from the subproblems. x = {372.664991614, 107.335008386}
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