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Simplifying 4u2 + 63u + 36 = 0 Reorder the terms: 36 + 63u + 4u2 = 0 Solving 36 + 63u + 4u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9 + 15.75u + u2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + 15.75u + -9 + u2 = 0 + -9 Reorder the terms: 9 + -9 + 15.75u + u2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 15.75u + u2 = 0 + -9 15.75u + u2 = 0 + -9 Combine like terms: 0 + -9 = -9 15.75u + u2 = -9 The u term is 15.75u. Take half its coefficient (7.875). Square it (62.015625) and add it to both sides. Add '62.015625' to each side of the equation. 15.75u + 62.015625 + u2 = -9 + 62.015625 Reorder the terms: 62.015625 + 15.75u + u2 = -9 + 62.015625 Combine like terms: -9 + 62.015625 = 53.015625 62.015625 + 15.75u + u2 = 53.015625 Factor a perfect square on the left side: (u + 7.875)(u + 7.875) = 53.015625 Calculate the square root of the right side: 7.28118294 Break this problem into two subproblems by setting (u + 7.875) equal to 7.28118294 and -7.28118294.Subproblem 1
u + 7.875 = 7.28118294 Simplifying u + 7.875 = 7.28118294 Reorder the terms: 7.875 + u = 7.28118294 Solving 7.875 + u = 7.28118294 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-7.875' to each side of the equation. 7.875 + -7.875 + u = 7.28118294 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + u = 7.28118294 + -7.875 u = 7.28118294 + -7.875 Combine like terms: 7.28118294 + -7.875 = -0.59381706 u = -0.59381706 Simplifying u = -0.59381706Subproblem 2
u + 7.875 = -7.28118294 Simplifying u + 7.875 = -7.28118294 Reorder the terms: 7.875 + u = -7.28118294 Solving 7.875 + u = -7.28118294 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-7.875' to each side of the equation. 7.875 + -7.875 + u = -7.28118294 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + u = -7.28118294 + -7.875 u = -7.28118294 + -7.875 Combine like terms: -7.28118294 + -7.875 = -15.15618294 u = -15.15618294 Simplifying u = -15.15618294Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.59381706, -15.15618294}
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