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Simplifying u2 + -18u = 23 Reorder the terms: -18u + u2 = 23 Solving -18u + u2 = 23 Solving for variable 'u'. Reorder the terms: -23 + -18u + u2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -18u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -18u + 23 + u2 = 0 + 23 Reorder the terms: -23 + 23 + -18u + u2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -18u + u2 = 0 + 23 -18u + u2 = 0 + 23 Combine like terms: 0 + 23 = 23 -18u + u2 = 23 The u term is -18u. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18u + 81 + u2 = 23 + 81 Reorder the terms: 81 + -18u + u2 = 23 + 81 Combine like terms: 23 + 81 = 104 81 + -18u + u2 = 104 Factor a perfect square on the left side: (u + -9)(u + -9) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (u + -9) equal to 10.198039027 and -10.198039027.Subproblem 1
u + -9 = 10.198039027 Simplifying u + -9 = 10.198039027 Reorder the terms: -9 + u = 10.198039027 Solving -9 + u = 10.198039027 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + u = 10.198039027 + 9 Combine like terms: -9 + 9 = 0 0 + u = 10.198039027 + 9 u = 10.198039027 + 9 Combine like terms: 10.198039027 + 9 = 19.198039027 u = 19.198039027 Simplifying u = 19.198039027Subproblem 2
u + -9 = -10.198039027 Simplifying u + -9 = -10.198039027 Reorder the terms: -9 + u = -10.198039027 Solving -9 + u = -10.198039027 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + u = -10.198039027 + 9 Combine like terms: -9 + 9 = 0 0 + u = -10.198039027 + 9 u = -10.198039027 + 9 Combine like terms: -10.198039027 + 9 = -1.198039027 u = -1.198039027 Simplifying u = -1.198039027Solution
The solution to the problem is based on the solutions from the subproblems. u = {19.198039027, -1.198039027}
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