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Simplifying u2 + -18u + -5 = 0 Reorder the terms: -5 + -18u + u2 = 0 Solving -5 + -18u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -18u + 5 + u2 = 0 + 5 Reorder the terms: -5 + 5 + -18u + u2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -18u + u2 = 0 + 5 -18u + u2 = 0 + 5 Combine like terms: 0 + 5 = 5 -18u + u2 = 5 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 = 5 + 81 Reorder the terms: 81 + -18u + u2 = 5 + 81 Combine like terms: 5 + 81 = 86 81 + -18u + u2 = 86 Factor a perfect square on the left side: (u + -9)(u + -9) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (u + -9) equal to 9.273618495 and -9.273618495.Subproblem 1
u + -9 = 9.273618495 Simplifying u + -9 = 9.273618495 Reorder the terms: -9 + u = 9.273618495 Solving -9 + u = 9.273618495 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 = 9.273618495 + 9 Combine like terms: -9 + 9 = 0 0 + u = 9.273618495 + 9 u = 9.273618495 + 9 Combine like terms: 9.273618495 + 9 = 18.273618495 u = 18.273618495 Simplifying u = 18.273618495Subproblem 2
u + -9 = -9.273618495 Simplifying u + -9 = -9.273618495 Reorder the terms: -9 + u = -9.273618495 Solving -9 + u = -9.273618495 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 = -9.273618495 + 9 Combine like terms: -9 + 9 = 0 0 + u = -9.273618495 + 9 u = -9.273618495 + 9 Combine like terms: -9.273618495 + 9 = -0.273618495 u = -0.273618495 Simplifying u = -0.273618495Solution
The solution to the problem is based on the solutions from the subproblems. u = {18.273618495, -0.273618495}
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