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Simplifying u2 + -4u + 4 + -80 = 0 Reorder the terms: 4 + -80 + -4u + u2 = 0 Combine like terms: 4 + -80 = -76 -76 + -4u + u2 = 0 Solving -76 + -4u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + -4u + 76 + u2 = 0 + 76 Reorder the terms: -76 + 76 + -4u + u2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + -4u + u2 = 0 + 76 -4u + u2 = 0 + 76 Combine like terms: 0 + 76 = 76 -4u + u2 = 76 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 = 76 + 4 Reorder the terms: 4 + -4u + u2 = 76 + 4 Combine like terms: 76 + 4 = 80 4 + -4u + u2 = 80 Factor a perfect square on the left side: (u + -2)(u + -2) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (u + -2) equal to 8.94427191 and -8.94427191.Subproblem 1
u + -2 = 8.94427191 Simplifying u + -2 = 8.94427191 Reorder the terms: -2 + u = 8.94427191 Solving -2 + u = 8.94427191 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 = 8.94427191 + 2 Combine like terms: -2 + 2 = 0 0 + u = 8.94427191 + 2 u = 8.94427191 + 2 Combine like terms: 8.94427191 + 2 = 10.94427191 u = 10.94427191 Simplifying u = 10.94427191Subproblem 2
u + -2 = -8.94427191 Simplifying u + -2 = -8.94427191 Reorder the terms: -2 + u = -8.94427191 Solving -2 + u = -8.94427191 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 = -8.94427191 + 2 Combine like terms: -2 + 2 = 0 0 + u = -8.94427191 + 2 u = -8.94427191 + 2 Combine like terms: -8.94427191 + 2 = -6.94427191 u = -6.94427191 Simplifying u = -6.94427191Solution
The solution to the problem is based on the solutions from the subproblems. u = {10.94427191, -6.94427191}
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