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Simplifying u2 + 18u + 20 = 0 Reorder the terms: 20 + 18u + u2 = 0 Solving 20 + 18u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 18u + -20 + u2 = 0 + -20 Reorder the terms: 20 + -20 + 18u + u2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 18u + u2 = 0 + -20 18u + u2 = 0 + -20 Combine like terms: 0 + -20 = -20 18u + u2 = -20 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 = -20 + 81 Reorder the terms: 81 + 18u + u2 = -20 + 81 Combine like terms: -20 + 81 = 61 81 + 18u + u2 = 61 Factor a perfect square on the left side: (u + 9)(u + 9) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (u + 9) equal to 7.810249676 and -7.810249676.Subproblem 1
u + 9 = 7.810249676 Simplifying u + 9 = 7.810249676 Reorder the terms: 9 + u = 7.810249676 Solving 9 + u = 7.810249676 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 = 7.810249676 + -9 Combine like terms: 9 + -9 = 0 0 + u = 7.810249676 + -9 u = 7.810249676 + -9 Combine like terms: 7.810249676 + -9 = -1.189750324 u = -1.189750324 Simplifying u = -1.189750324Subproblem 2
u + 9 = -7.810249676 Simplifying u + 9 = -7.810249676 Reorder the terms: 9 + u = -7.810249676 Solving 9 + u = -7.810249676 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 = -7.810249676 + -9 Combine like terms: 9 + -9 = 0 0 + u = -7.810249676 + -9 u = -7.810249676 + -9 Combine like terms: -7.810249676 + -9 = -16.810249676 u = -16.810249676 Simplifying u = -16.810249676Solution
The solution to the problem is based on the solutions from the subproblems. u = {-1.189750324, -16.810249676}
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