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Simplifying u2 + -10u = 47 Reorder the terms: -10u + u2 = 47 Solving -10u + u2 = 47 Solving for variable 'u'. Reorder the terms: -47 + -10u + u2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + -10u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -10u + 47 + u2 = 0 + 47 Reorder the terms: -47 + 47 + -10u + u2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -10u + u2 = 0 + 47 -10u + u2 = 0 + 47 Combine like terms: 0 + 47 = 47 -10u + u2 = 47 The u term is -10u. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10u + 25 + u2 = 47 + 25 Reorder the terms: 25 + -10u + u2 = 47 + 25 Combine like terms: 47 + 25 = 72 25 + -10u + u2 = 72 Factor a perfect square on the left side: (u + -5)(u + -5) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (u + -5) equal to 8.485281374 and -8.485281374.Subproblem 1
u + -5 = 8.485281374 Simplifying u + -5 = 8.485281374 Reorder the terms: -5 + u = 8.485281374 Solving -5 + u = 8.485281374 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + u = 8.485281374 + 5 Combine like terms: -5 + 5 = 0 0 + u = 8.485281374 + 5 u = 8.485281374 + 5 Combine like terms: 8.485281374 + 5 = 13.485281374 u = 13.485281374 Simplifying u = 13.485281374Subproblem 2
u + -5 = -8.485281374 Simplifying u + -5 = -8.485281374 Reorder the terms: -5 + u = -8.485281374 Solving -5 + u = -8.485281374 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + u = -8.485281374 + 5 Combine like terms: -5 + 5 = 0 0 + u = -8.485281374 + 5 u = -8.485281374 + 5 Combine like terms: -8.485281374 + 5 = -3.485281374 u = -3.485281374 Simplifying u = -3.485281374Solution
The solution to the problem is based on the solutions from the subproblems. u = {13.485281374, -3.485281374}
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