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Simplifying 12500 = 0.5x2 + 11x + 4000 Reorder the terms: 12500 = 4000 + 11x + 0.5x2 Solving 12500 = 4000 + 11x + 0.5x2 Solving for variable 'x'. Combine like terms: 12500 + -4000 = 8500 8500 + -11x + -0.5x2 = 4000 + 11x + 0.5x2 + -4000 + -11x + -0.5x2 Reorder the terms: 8500 + -11x + -0.5x2 = 4000 + -4000 + 11x + -11x + 0.5x2 + -0.5x2 Combine like terms: 4000 + -4000 = 0 8500 + -11x + -0.5x2 = 0 + 11x + -11x + 0.5x2 + -0.5x2 8500 + -11x + -0.5x2 = 11x + -11x + 0.5x2 + -0.5x2 Combine like terms: 11x + -11x = 0 8500 + -11x + -0.5x2 = 0 + 0.5x2 + -0.5x2 8500 + -11x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 8500 + -11x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -17000 + 22x + x2 = 0 Move the constant term to the right: Add '17000' to each side of the equation. -17000 + 22x + 17000 + x2 = 0 + 17000 Reorder the terms: -17000 + 17000 + 22x + x2 = 0 + 17000 Combine like terms: -17000 + 17000 = 0 0 + 22x + x2 = 0 + 17000 22x + x2 = 0 + 17000 Combine like terms: 0 + 17000 = 17000 22x + x2 = 17000 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 17000 + 121 Reorder the terms: 121 + 22x + x2 = 17000 + 121 Combine like terms: 17000 + 121 = 17121 121 + 22x + x2 = 17121 Factor a perfect square on the left side: (x + 11)(x + 11) = 17121 Calculate the square root of the right side: 130.847239176 Break this problem into two subproblems by setting (x + 11) equal to 130.847239176 and -130.847239176.Subproblem 1
x + 11 = 130.847239176 Simplifying x + 11 = 130.847239176 Reorder the terms: 11 + x = 130.847239176 Solving 11 + x = 130.847239176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 130.847239176 + -11 Combine like terms: 11 + -11 = 0 0 + x = 130.847239176 + -11 x = 130.847239176 + -11 Combine like terms: 130.847239176 + -11 = 119.847239176 x = 119.847239176 Simplifying x = 119.847239176Subproblem 2
x + 11 = -130.847239176 Simplifying x + 11 = -130.847239176 Reorder the terms: 11 + x = -130.847239176 Solving 11 + x = -130.847239176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -130.847239176 + -11 Combine like terms: 11 + -11 = 0 0 + x = -130.847239176 + -11 x = -130.847239176 + -11 Combine like terms: -130.847239176 + -11 = -141.847239176 x = -141.847239176 Simplifying x = -141.847239176Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.847239176, -141.847239176}
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