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Simplifying 0.025x2 + 250x + -2532 = 0 Reorder the terms: -2532 + 250x + 0.025x2 = 0 Solving -2532 + 250x + 0.025x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.025 the coefficient of the squared term: Divide each side by '0.025'. -101280 + 10000x + x2 = 0 Move the constant term to the right: Add '101280' to each side of the equation. -101280 + 10000x + 101280 + x2 = 0 + 101280 Reorder the terms: -101280 + 101280 + 10000x + x2 = 0 + 101280 Combine like terms: -101280 + 101280 = 0 0 + 10000x + x2 = 0 + 101280 10000x + x2 = 0 + 101280 Combine like terms: 0 + 101280 = 101280 10000x + x2 = 101280 The x term is 10000x. Take half its coefficient (5000). Square it (25000000) and add it to both sides. Add '25000000' to each side of the equation. 10000x + 25000000 + x2 = 101280 + 25000000 Reorder the terms: 25000000 + 10000x + x2 = 101280 + 25000000 Combine like terms: 101280 + 25000000 = 25101280 25000000 + 10000x + x2 = 25101280 Factor a perfect square on the left side: (x + 5000)(x + 5000) = 25101280 Calculate the square root of the right side: 5010.117763087 Break this problem into two subproblems by setting (x + 5000) equal to 5010.117763087 and -5010.117763087.Subproblem 1
x + 5000 = 5010.117763087 Simplifying x + 5000 = 5010.117763087 Reorder the terms: 5000 + x = 5010.117763087 Solving 5000 + x = 5010.117763087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5000' to each side of the equation. 5000 + -5000 + x = 5010.117763087 + -5000 Combine like terms: 5000 + -5000 = 0 0 + x = 5010.117763087 + -5000 x = 5010.117763087 + -5000 Combine like terms: 5010.117763087 + -5000 = 10.117763087 x = 10.117763087 Simplifying x = 10.117763087Subproblem 2
x + 5000 = -5010.117763087 Simplifying x + 5000 = -5010.117763087 Reorder the terms: 5000 + x = -5010.117763087 Solving 5000 + x = -5010.117763087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5000' to each side of the equation. 5000 + -5000 + x = -5010.117763087 + -5000 Combine like terms: 5000 + -5000 = 0 0 + x = -5010.117763087 + -5000 x = -5010.117763087 + -5000 Combine like terms: -5010.117763087 + -5000 = -10010.117763087 x = -10010.117763087 Simplifying x = -10010.117763087Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.117763087, -10010.117763087}
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