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Simplifying u2 + -12u = 54 Reorder the terms: -12u + u2 = 54 Solving -12u + u2 = 54 Solving for variable 'u'. Reorder the terms: -54 + -12u + u2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + -12u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -12u + 54 + u2 = 0 + 54 Reorder the terms: -54 + 54 + -12u + u2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -12u + u2 = 0 + 54 -12u + u2 = 0 + 54 Combine like terms: 0 + 54 = 54 -12u + u2 = 54 The u term is -12u. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12u + 36 + u2 = 54 + 36 Reorder the terms: 36 + -12u + u2 = 54 + 36 Combine like terms: 54 + 36 = 90 36 + -12u + u2 = 90 Factor a perfect square on the left side: (u + -6)(u + -6) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (u + -6) equal to 9.486832981 and -9.486832981.Subproblem 1
u + -6 = 9.486832981 Simplifying u + -6 = 9.486832981 Reorder the terms: -6 + u = 9.486832981 Solving -6 + u = 9.486832981 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + u = 9.486832981 + 6 Combine like terms: -6 + 6 = 0 0 + u = 9.486832981 + 6 u = 9.486832981 + 6 Combine like terms: 9.486832981 + 6 = 15.486832981 u = 15.486832981 Simplifying u = 15.486832981Subproblem 2
u + -6 = -9.486832981 Simplifying u + -6 = -9.486832981 Reorder the terms: -6 + u = -9.486832981 Solving -6 + u = -9.486832981 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + u = -9.486832981 + 6 Combine like terms: -6 + 6 = 0 0 + u = -9.486832981 + 6 u = -9.486832981 + 6 Combine like terms: -9.486832981 + 6 = -3.486832981 u = -3.486832981 Simplifying u = -3.486832981Solution
The solution to the problem is based on the solutions from the subproblems. u = {15.486832981, -3.486832981}
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