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Simplifying 2500 + 4.8x + 0.002x2 = 10500 Solving 2500 + 4.8x + 0.002x2 = 10500 Solving for variable 'x'. Reorder the terms: 2500 + -10500 + 4.8x + 0.002x2 = 10500 + -10500 Combine like terms: 2500 + -10500 = -8000 -8000 + 4.8x + 0.002x2 = 10500 + -10500 Combine like terms: 10500 + -10500 = 0 -8000 + 4.8x + 0.002x2 = 0 Begin completing the square. Divide all terms by 0.002 the coefficient of the squared term: Divide each side by '0.002'. -4000000 + 2400x + x2 = 0 Move the constant term to the right: Add '4000000' to each side of the equation. -4000000 + 2400x + 4000000 + x2 = 0 + 4000000 Reorder the terms: -4000000 + 4000000 + 2400x + x2 = 0 + 4000000 Combine like terms: -4000000 + 4000000 = 0 0 + 2400x + x2 = 0 + 4000000 2400x + x2 = 0 + 4000000 Combine like terms: 0 + 4000000 = 4000000 2400x + x2 = 4000000 The x term is 2400x. Take half its coefficient (1200). Square it (1440000) and add it to both sides. Add '1440000' to each side of the equation. 2400x + 1440000 + x2 = 4000000 + 1440000 Reorder the terms: 1440000 + 2400x + x2 = 4000000 + 1440000 Combine like terms: 4000000 + 1440000 = 5440000 1440000 + 2400x + x2 = 5440000 Factor a perfect square on the left side: (x + 1200)(x + 1200) = 5440000 Calculate the square root of the right side: 2332.380757938 Break this problem into two subproblems by setting (x + 1200) equal to 2332.380757938 and -2332.380757938.Subproblem 1
x + 1200 = 2332.380757938 Simplifying x + 1200 = 2332.380757938 Reorder the terms: 1200 + x = 2332.380757938 Solving 1200 + x = 2332.380757938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1200' to each side of the equation. 1200 + -1200 + x = 2332.380757938 + -1200 Combine like terms: 1200 + -1200 = 0 0 + x = 2332.380757938 + -1200 x = 2332.380757938 + -1200 Combine like terms: 2332.380757938 + -1200 = 1132.380757938 x = 1132.380757938 Simplifying x = 1132.380757938Subproblem 2
x + 1200 = -2332.380757938 Simplifying x + 1200 = -2332.380757938 Reorder the terms: 1200 + x = -2332.380757938 Solving 1200 + x = -2332.380757938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1200' to each side of the equation. 1200 + -1200 + x = -2332.380757938 + -1200 Combine like terms: 1200 + -1200 = 0 0 + x = -2332.380757938 + -1200 x = -2332.380757938 + -1200 Combine like terms: -2332.380757938 + -1200 = -3532.380757938 x = -3532.380757938 Simplifying x = -3532.380757938Solution
The solution to the problem is based on the solutions from the subproblems. x = {1132.380757938, -3532.380757938}
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