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Simplifying u2 + -9u + 4 = 0 Reorder the terms: 4 + -9u + u2 = 0 Solving 4 + -9u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -9u + -4 + u2 = 0 + -4 Reorder the terms: 4 + -4 + -9u + u2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9u + u2 = 0 + -4 -9u + u2 = 0 + -4 Combine like terms: 0 + -4 = -4 -9u + u2 = -4 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 = -4 + 20.25 Reorder the terms: 20.25 + -9u + u2 = -4 + 20.25 Combine like terms: -4 + 20.25 = 16.25 20.25 + -9u + u2 = 16.25 Factor a perfect square on the left side: (u + -4.5)(u + -4.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (u + -4.5) equal to 4.031128874 and -4.031128874.Subproblem 1
u + -4.5 = 4.031128874 Simplifying u + -4.5 = 4.031128874 Reorder the terms: -4.5 + u = 4.031128874 Solving -4.5 + u = 4.031128874 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 = 4.031128874 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = 4.031128874 + 4.5 u = 4.031128874 + 4.5 Combine like terms: 4.031128874 + 4.5 = 8.531128874 u = 8.531128874 Simplifying u = 8.531128874Subproblem 2
u + -4.5 = -4.031128874 Simplifying u + -4.5 = -4.031128874 Reorder the terms: -4.5 + u = -4.031128874 Solving -4.5 + u = -4.031128874 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 = -4.031128874 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = -4.031128874 + 4.5 u = -4.031128874 + 4.5 Combine like terms: -4.031128874 + 4.5 = 0.468871126 u = 0.468871126 Simplifying u = 0.468871126Solution
The solution to the problem is based on the solutions from the subproblems. u = {8.531128874, 0.468871126}
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