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Simplifying 5u = u2 + -4 Reorder the terms: 5u = -4 + u2 Solving 5u = -4 + u2 Solving for variable 'u'. Reorder the terms: 4 + 5u + -1u2 = -4 + u2 + 4 + -1u2 Reorder the terms: 4 + 5u + -1u2 = -4 + 4 + u2 + -1u2 Combine like terms: -4 + 4 = 0 4 + 5u + -1u2 = 0 + u2 + -1u2 4 + 5u + -1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 4 + 5u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -5u + u2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -5u + 4 + u2 = 0 + 4 Reorder the terms: -4 + 4 + -5u + u2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5u + u2 = 0 + 4 -5u + u2 = 0 + 4 Combine like terms: 0 + 4 = 4 -5u + u2 = 4 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 = 4 + 6.25 Reorder the terms: 6.25 + -5u + u2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + -5u + u2 = 10.25 Factor a perfect square on the left side: (u + -2.5)(u + -2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (u + -2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
u + -2.5 = 3.201562119 Simplifying u + -2.5 = 3.201562119 Reorder the terms: -2.5 + u = 3.201562119 Solving -2.5 + u = 3.201562119 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 = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = 3.201562119 + 2.5 u = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 u = 5.701562119 Simplifying u = 5.701562119Subproblem 2
u + -2.5 = -3.201562119 Simplifying u + -2.5 = -3.201562119 Reorder the terms: -2.5 + u = -3.201562119 Solving -2.5 + u = -3.201562119 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 = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = -3.201562119 + 2.5 u = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 u = -0.701562119 Simplifying u = -0.701562119Solution
The solution to the problem is based on the solutions from the subproblems. u = {5.701562119, -0.701562119}
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