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Simplifying u2 + 4u + -23 = 0 Reorder the terms: -23 + 4u + u2 = 0 Solving -23 + 4u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 4u + 23 + u2 = 0 + 23 Reorder the terms: -23 + 23 + 4u + u2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 4u + u2 = 0 + 23 4u + u2 = 0 + 23 Combine like terms: 0 + 23 = 23 4u + u2 = 23 The u term is 4u. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4u + 4 + u2 = 23 + 4 Reorder the terms: 4 + 4u + u2 = 23 + 4 Combine like terms: 23 + 4 = 27 4 + 4u + u2 = 27 Factor a perfect square on the left side: (u + 2)(u + 2) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (u + 2) equal to 5.196152423 and -5.196152423.Subproblem 1
u + 2 = 5.196152423 Simplifying u + 2 = 5.196152423 Reorder the terms: 2 + u = 5.196152423 Solving 2 + u = 5.196152423 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + u = 5.196152423 + -2 Combine like terms: 2 + -2 = 0 0 + u = 5.196152423 + -2 u = 5.196152423 + -2 Combine like terms: 5.196152423 + -2 = 3.196152423 u = 3.196152423 Simplifying u = 3.196152423Subproblem 2
u + 2 = -5.196152423 Simplifying u + 2 = -5.196152423 Reorder the terms: 2 + u = -5.196152423 Solving 2 + u = -5.196152423 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + u = -5.196152423 + -2 Combine like terms: 2 + -2 = 0 0 + u = -5.196152423 + -2 u = -5.196152423 + -2 Combine like terms: -5.196152423 + -2 = -7.196152423 u = -7.196152423 Simplifying u = -7.196152423Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.196152423, -7.196152423}
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