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Simplifying u2 + u + -5 = 0 Reorder the terms: -5 + u + u2 = 0 Solving -5 + u + 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 + u + 5 + u2 = 0 + 5 Reorder the terms: -5 + 5 + u + u2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + u + u2 = 0 + 5 u + u2 = 0 + 5 Combine like terms: 0 + 5 = 5 u + u2 = 5 The u term is u. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. u + 0.25 + u2 = 5 + 0.25 Reorder the terms: 0.25 + u + u2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + u + u2 = 5.25 Factor a perfect square on the left side: (u + 0.5)(u + 0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (u + 0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
u + 0.5 = 2.291287847 Simplifying u + 0.5 = 2.291287847 Reorder the terms: 0.5 + u = 2.291287847 Solving 0.5 + u = 2.291287847 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + u = 2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = 2.291287847 + -0.5 u = 2.291287847 + -0.5 Combine like terms: 2.291287847 + -0.5 = 1.791287847 u = 1.791287847 Simplifying u = 1.791287847Subproblem 2
u + 0.5 = -2.291287847 Simplifying u + 0.5 = -2.291287847 Reorder the terms: 0.5 + u = -2.291287847 Solving 0.5 + u = -2.291287847 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + u = -2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = -2.291287847 + -0.5 u = -2.291287847 + -0.5 Combine like terms: -2.291287847 + -0.5 = -2.791287847 u = -2.791287847 Simplifying u = -2.791287847Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.791287847, -2.791287847}
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