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Simplifying (u + 3)(u + 3) + 7 = 97 Reorder the terms: (3 + u)(u + 3) + 7 = 97 Reorder the terms: (3 + u)(3 + u) + 7 = 97 Multiply (3 + u) * (3 + u) (3(3 + u) + u(3 + u)) + 7 = 97 ((3 * 3 + u * 3) + u(3 + u)) + 7 = 97 ((9 + 3u) + u(3 + u)) + 7 = 97 (9 + 3u + (3 * u + u * u)) + 7 = 97 (9 + 3u + (3u + u2)) + 7 = 97 Combine like terms: 3u + 3u = 6u (9 + 6u + u2) + 7 = 97 Reorder the terms: 9 + 7 + 6u + u2 = 97 Combine like terms: 9 + 7 = 16 16 + 6u + u2 = 97 Solving 16 + 6u + u2 = 97 Solving for variable 'u'. Reorder the terms: 16 + -97 + 6u + u2 = 97 + -97 Combine like terms: 16 + -97 = -81 -81 + 6u + u2 = 97 + -97 Combine like terms: 97 + -97 = 0 -81 + 6u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 6u + 81 + u2 = 0 + 81 Reorder the terms: -81 + 81 + 6u + u2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 6u + u2 = 0 + 81 6u + u2 = 0 + 81 Combine like terms: 0 + 81 = 81 6u + u2 = 81 The u term is 6u. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6u + 9 + u2 = 81 + 9 Reorder the terms: 9 + 6u + u2 = 81 + 9 Combine like terms: 81 + 9 = 90 9 + 6u + u2 = 90 Factor a perfect square on the left side: (u + 3)(u + 3) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (u + 3) equal to 9.486832981 and -9.486832981.Subproblem 1
u + 3 = 9.486832981 Simplifying u + 3 = 9.486832981 Reorder the terms: 3 + u = 9.486832981 Solving 3 + u = 9.486832981 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = 9.486832981 + -3 Combine like terms: 3 + -3 = 0 0 + u = 9.486832981 + -3 u = 9.486832981 + -3 Combine like terms: 9.486832981 + -3 = 6.486832981 u = 6.486832981 Simplifying u = 6.486832981Subproblem 2
u + 3 = -9.486832981 Simplifying u + 3 = -9.486832981 Reorder the terms: 3 + u = -9.486832981 Solving 3 + u = -9.486832981 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = -9.486832981 + -3 Combine like terms: 3 + -3 = 0 0 + u = -9.486832981 + -3 u = -9.486832981 + -3 Combine like terms: -9.486832981 + -3 = -12.486832981 u = -12.486832981 Simplifying u = -12.486832981Solution
The solution to the problem is based on the solutions from the subproblems. u = {6.486832981, -12.486832981}
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