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Simplifying 1250u2 + -62.5u + -9 = 0 Reorder the terms: -9 + -62.5u + 1250u2 = 0 Solving -9 + -62.5u + 1250u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 1250 the coefficient of the squared term: Divide each side by '1250'. -0.0072 + -0.05u + u2 = 0 Move the constant term to the right: Add '0.0072' to each side of the equation. -0.0072 + -0.05u + 0.0072 + u2 = 0 + 0.0072 Reorder the terms: -0.0072 + 0.0072 + -0.05u + u2 = 0 + 0.0072 Combine like terms: -0.0072 + 0.0072 = 0.0000 0.0000 + -0.05u + u2 = 0 + 0.0072 -0.05u + u2 = 0 + 0.0072 Combine like terms: 0 + 0.0072 = 0.0072 -0.05u + u2 = 0.0072 The u term is -0.05u. Take half its coefficient (-0.025). Square it (0.000625) and add it to both sides. Add '0.000625' to each side of the equation. -0.05u + 0.000625 + u2 = 0.0072 + 0.000625 Reorder the terms: 0.000625 + -0.05u + u2 = 0.0072 + 0.000625 Combine like terms: 0.0072 + 0.000625 = 0.007825 0.000625 + -0.05u + u2 = 0.007825 Factor a perfect square on the left side: (u + -0.025)(u + -0.025) = 0.007825 Calculate the square root of the right side: 0.08845903 Break this problem into two subproblems by setting (u + -0.025) equal to 0.08845903 and -0.08845903.Subproblem 1
u + -0.025 = 0.08845903 Simplifying u + -0.025 = 0.08845903 Reorder the terms: -0.025 + u = 0.08845903 Solving -0.025 + u = 0.08845903 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + u = 0.08845903 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + u = 0.08845903 + 0.025 u = 0.08845903 + 0.025 Combine like terms: 0.08845903 + 0.025 = 0.11345903 u = 0.11345903 Simplifying u = 0.11345903Subproblem 2
u + -0.025 = -0.08845903 Simplifying u + -0.025 = -0.08845903 Reorder the terms: -0.025 + u = -0.08845903 Solving -0.025 + u = -0.08845903 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + u = -0.08845903 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + u = -0.08845903 + 0.025 u = -0.08845903 + 0.025 Combine like terms: -0.08845903 + 0.025 = -0.06345903 u = -0.06345903 Simplifying u = -0.06345903Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.11345903, -0.06345903}
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