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Simplifying u2 + -5u + -10 = 0 Reorder the terms: -10 + -5u + u2 = 0 Solving -10 + -5u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -5u + 10 + u2 = 0 + 10 Reorder the terms: -10 + 10 + -5u + u2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -5u + u2 = 0 + 10 -5u + u2 = 0 + 10 Combine like terms: 0 + 10 = 10 -5u + u2 = 10 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 = 10 + 6.25 Reorder the terms: 6.25 + -5u + u2 = 10 + 6.25 Combine like terms: 10 + 6.25 = 16.25 6.25 + -5u + u2 = 16.25 Factor a perfect square on the left side: (u + -2.5)(u + -2.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (u + -2.5) equal to 4.031128874 and -4.031128874.Subproblem 1
u + -2.5 = 4.031128874 Simplifying u + -2.5 = 4.031128874 Reorder the terms: -2.5 + u = 4.031128874 Solving -2.5 + u = 4.031128874 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 = 4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = 4.031128874 + 2.5 u = 4.031128874 + 2.5 Combine like terms: 4.031128874 + 2.5 = 6.531128874 u = 6.531128874 Simplifying u = 6.531128874Subproblem 2
u + -2.5 = -4.031128874 Simplifying u + -2.5 = -4.031128874 Reorder the terms: -2.5 + u = -4.031128874 Solving -2.5 + u = -4.031128874 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 = -4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = -4.031128874 + 2.5 u = -4.031128874 + 2.5 Combine like terms: -4.031128874 + 2.5 = -1.531128874 u = -1.531128874 Simplifying u = -1.531128874Solution
The solution to the problem is based on the solutions from the subproblems. u = {6.531128874, -1.531128874}
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