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Simplifying -1u2 + -8u + 4 = 0 Reorder the terms: 4 + -8u + -1u2 = 0 Solving 4 + -8u + -1u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 8u + u2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 8u + 4 + u2 = 0 + 4 Reorder the terms: -4 + 4 + 8u + u2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 8u + u2 = 0 + 4 8u + u2 = 0 + 4 Combine like terms: 0 + 4 = 4 8u + u2 = 4 The u term is 8u. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8u + 16 + u2 = 4 + 16 Reorder the terms: 16 + 8u + u2 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + 8u + u2 = 20 Factor a perfect square on the left side: (u + 4)(u + 4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (u + 4) equal to 4.472135955 and -4.472135955.Subproblem 1
u + 4 = 4.472135955 Simplifying u + 4 = 4.472135955 Reorder the terms: 4 + u = 4.472135955 Solving 4 + u = 4.472135955 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + u = 4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + u = 4.472135955 + -4 u = 4.472135955 + -4 Combine like terms: 4.472135955 + -4 = 0.472135955 u = 0.472135955 Simplifying u = 0.472135955Subproblem 2
u + 4 = -4.472135955 Simplifying u + 4 = -4.472135955 Reorder the terms: 4 + u = -4.472135955 Solving 4 + u = -4.472135955 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + u = -4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + u = -4.472135955 + -4 u = -4.472135955 + -4 Combine like terms: -4.472135955 + -4 = -8.472135955 u = -8.472135955 Simplifying u = -8.472135955Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.472135955, -8.472135955}
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