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Simplifying 5000 + 25x + -0.001x2 = 0 Solving 5000 + 25x + -0.001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.001 the coefficient of the squared term: Divide each side by '-0.001'. -5000000 + -25000x + x2 = 0 Move the constant term to the right: Add '5000000' to each side of the equation. -5000000 + -25000x + 5000000 + x2 = 0 + 5000000 Reorder the terms: -5000000 + 5000000 + -25000x + x2 = 0 + 5000000 Combine like terms: -5000000 + 5000000 = 0 0 + -25000x + x2 = 0 + 5000000 -25000x + x2 = 0 + 5000000 Combine like terms: 0 + 5000000 = 5000000 -25000x + x2 = 5000000 The x term is -25000x. Take half its coefficient (-12500). Square it (156250000) and add it to both sides. Add '156250000' to each side of the equation. -25000x + 156250000 + x2 = 5000000 + 156250000 Reorder the terms: 156250000 + -25000x + x2 = 5000000 + 156250000 Combine like terms: 5000000 + 156250000 = 161250000 156250000 + -25000x + x2 = 161250000 Factor a perfect square on the left side: (x + -12500)(x + -12500) = 161250000 Calculate the square root of the right side: 12698.4250992 Break this problem into two subproblems by setting (x + -12500) equal to 12698.4250992 and -12698.4250992.Subproblem 1
x + -12500 = 12698.4250992 Simplifying x + -12500 = 12698.4250992 Reorder the terms: -12500 + x = 12698.4250992 Solving -12500 + x = 12698.4250992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12500' to each side of the equation. -12500 + 12500 + x = 12698.4250992 + 12500 Combine like terms: -12500 + 12500 = 0 0 + x = 12698.4250992 + 12500 x = 12698.4250992 + 12500 Combine like terms: 12698.4250992 + 12500 = 25198.4250992 x = 25198.4250992 Simplifying x = 25198.4250992Subproblem 2
x + -12500 = -12698.4250992 Simplifying x + -12500 = -12698.4250992 Reorder the terms: -12500 + x = -12698.4250992 Solving -12500 + x = -12698.4250992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12500' to each side of the equation. -12500 + 12500 + x = -12698.4250992 + 12500 Combine like terms: -12500 + 12500 = 0 0 + x = -12698.4250992 + 12500 x = -12698.4250992 + 12500 Combine like terms: -12698.4250992 + 12500 = -198.4250992 x = -198.4250992 Simplifying x = -198.4250992Solution
The solution to the problem is based on the solutions from the subproblems. x = {25198.4250992, -198.4250992}
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