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Simplifying u2 + -5u + -18 = 0 Reorder the terms: -18 + -5u + u2 = 0 Solving -18 + -5u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -5u + 18 + u2 = 0 + 18 Reorder the terms: -18 + 18 + -5u + u2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -5u + u2 = 0 + 18 -5u + u2 = 0 + 18 Combine like terms: 0 + 18 = 18 -5u + u2 = 18 The u term is -5u. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5u + 6.25 + u2 = 18 + 6.25 Reorder the terms: 6.25 + -5u + u2 = 18 + 6.25 Combine like terms: 18 + 6.25 = 24.25 6.25 + -5u + u2 = 24.25 Factor a perfect square on the left side: (u + -2.5)(u + -2.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (u + -2.5) equal to 4.924428901 and -4.924428901.Subproblem 1
u + -2.5 = 4.924428901 Simplifying u + -2.5 = 4.924428901 Reorder the terms: -2.5 + u = 4.924428901 Solving -2.5 + u = 4.924428901 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + u = 4.924428901 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = 4.924428901 + 2.5 u = 4.924428901 + 2.5 Combine like terms: 4.924428901 + 2.5 = 7.424428901 u = 7.424428901 Simplifying u = 7.424428901Subproblem 2
u + -2.5 = -4.924428901 Simplifying u + -2.5 = -4.924428901 Reorder the terms: -2.5 + u = -4.924428901 Solving -2.5 + u = -4.924428901 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + u = -4.924428901 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = -4.924428901 + 2.5 u = -4.924428901 + 2.5 Combine like terms: -4.924428901 + 2.5 = -2.424428901 u = -2.424428901 Simplifying u = -2.424428901Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.424428901, -2.424428901}
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