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Simplifying u2 + -9u + 5 = 0 Reorder the terms: 5 + -9u + u2 = 0 Solving 5 + -9u + 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 + -9u + -5 + u2 = 0 + -5 Reorder the terms: 5 + -5 + -9u + u2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9u + u2 = 0 + -5 -9u + u2 = 0 + -5 Combine like terms: 0 + -5 = -5 -9u + u2 = -5 The u term is -9u. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9u + 20.25 + u2 = -5 + 20.25 Reorder the terms: 20.25 + -9u + u2 = -5 + 20.25 Combine like terms: -5 + 20.25 = 15.25 20.25 + -9u + u2 = 15.25 Factor a perfect square on the left side: (u + -4.5)(u + -4.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (u + -4.5) equal to 3.905124838 and -3.905124838.Subproblem 1
u + -4.5 = 3.905124838 Simplifying u + -4.5 = 3.905124838 Reorder the terms: -4.5 + u = 3.905124838 Solving -4.5 + u = 3.905124838 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + u = 3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = 3.905124838 + 4.5 u = 3.905124838 + 4.5 Combine like terms: 3.905124838 + 4.5 = 8.405124838 u = 8.405124838 Simplifying u = 8.405124838Subproblem 2
u + -4.5 = -3.905124838 Simplifying u + -4.5 = -3.905124838 Reorder the terms: -4.5 + u = -3.905124838 Solving -4.5 + u = -3.905124838 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + u = -3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = -3.905124838 + 4.5 u = -3.905124838 + 4.5 Combine like terms: -3.905124838 + 4.5 = 0.594875162 u = 0.594875162 Simplifying u = 0.594875162Solution
The solution to the problem is based on the solutions from the subproblems. u = {8.405124838, 0.594875162}
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