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Simplifying 1285 = 0.08x2 + 51x Reorder the terms: 1285 = 51x + 0.08x2 Solving 1285 = 51x + 0.08x2 Solving for variable 'x'. Reorder the terms: 1285 + -51x + -0.08x2 = 51x + -51x + 0.08x2 + -0.08x2 Combine like terms: 51x + -51x = 0 1285 + -51x + -0.08x2 = 0 + 0.08x2 + -0.08x2 1285 + -51x + -0.08x2 = 0.08x2 + -0.08x2 Combine like terms: 0.08x2 + -0.08x2 = 0.00 1285 + -51x + -0.08x2 = 0.00 Begin completing the square. Divide all terms by -0.08 the coefficient of the squared term: Divide each side by '-0.08'. -16062.5 + 637.5x + x2 = 0 Move the constant term to the right: Add '16062.5' to each side of the equation. -16062.5 + 637.5x + 16062.5 + x2 = 0 + 16062.5 Reorder the terms: -16062.5 + 16062.5 + 637.5x + x2 = 0 + 16062.5 Combine like terms: -16062.5 + 16062.5 = 0.0 0.0 + 637.5x + x2 = 0 + 16062.5 637.5x + x2 = 0 + 16062.5 Combine like terms: 0 + 16062.5 = 16062.5 637.5x + x2 = 16062.5 The x term is 637.5x. Take half its coefficient (318.75). Square it (101601.5625) and add it to both sides. Add '101601.5625' to each side of the equation. 637.5x + 101601.5625 + x2 = 16062.5 + 101601.5625 Reorder the terms: 101601.5625 + 637.5x + x2 = 16062.5 + 101601.5625 Combine like terms: 16062.5 + 101601.5625 = 117664.0625 101601.5625 + 637.5x + x2 = 117664.0625 Factor a perfect square on the left side: (x + 318.75)(x + 318.75) = 117664.0625 Calculate the square root of the right side: 343.021956294 Break this problem into two subproblems by setting (x + 318.75) equal to 343.021956294 and -343.021956294.Subproblem 1
x + 318.75 = 343.021956294 Simplifying x + 318.75 = 343.021956294 Reorder the terms: 318.75 + x = 343.021956294 Solving 318.75 + x = 343.021956294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-318.75' to each side of the equation. 318.75 + -318.75 + x = 343.021956294 + -318.75 Combine like terms: 318.75 + -318.75 = 0.00 0.00 + x = 343.021956294 + -318.75 x = 343.021956294 + -318.75 Combine like terms: 343.021956294 + -318.75 = 24.271956294 x = 24.271956294 Simplifying x = 24.271956294Subproblem 2
x + 318.75 = -343.021956294 Simplifying x + 318.75 = -343.021956294 Reorder the terms: 318.75 + x = -343.021956294 Solving 318.75 + x = -343.021956294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-318.75' to each side of the equation. 318.75 + -318.75 + x = -343.021956294 + -318.75 Combine like terms: 318.75 + -318.75 = 0.00 0.00 + x = -343.021956294 + -318.75 x = -343.021956294 + -318.75 Combine like terms: -343.021956294 + -318.75 = -661.771956294 x = -661.771956294 Simplifying x = -661.771956294Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.271956294, -661.771956294}
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