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Simplifying u2 + -5u + 1 = 0 Reorder the terms: 1 + -5u + u2 = 0 Solving 1 + -5u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5u + -1 + u2 = 0 + -1 Reorder the terms: 1 + -1 + -5u + u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5u + u2 = 0 + -1 -5u + u2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5u + u2 = -1 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 = -1 + 6.25 Reorder the terms: 6.25 + -5u + u2 = -1 + 6.25 Combine like terms: -1 + 6.25 = 5.25 6.25 + -5u + u2 = 5.25 Factor a perfect square on the left side: (u + -2.5)(u + -2.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (u + -2.5) equal to 2.291287847 and -2.291287847.Subproblem 1
u + -2.5 = 2.291287847 Simplifying u + -2.5 = 2.291287847 Reorder the terms: -2.5 + u = 2.291287847 Solving -2.5 + u = 2.291287847 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 = 2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = 2.291287847 + 2.5 u = 2.291287847 + 2.5 Combine like terms: 2.291287847 + 2.5 = 4.791287847 u = 4.791287847 Simplifying u = 4.791287847Subproblem 2
u + -2.5 = -2.291287847 Simplifying u + -2.5 = -2.291287847 Reorder the terms: -2.5 + u = -2.291287847 Solving -2.5 + u = -2.291287847 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 = -2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = -2.291287847 + 2.5 u = -2.291287847 + 2.5 Combine like terms: -2.291287847 + 2.5 = 0.208712153 u = 0.208712153 Simplifying u = 0.208712153Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.791287847, 0.208712153}
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