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Simplifying u2 + -8u = 41 Reorder the terms: -8u + u2 = 41 Solving -8u + u2 = 41 Solving for variable 'u'. Reorder the terms: -41 + -8u + u2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + -8u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -8u + 41 + u2 = 0 + 41 Reorder the terms: -41 + 41 + -8u + u2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -8u + u2 = 0 + 41 -8u + u2 = 0 + 41 Combine like terms: 0 + 41 = 41 -8u + u2 = 41 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 = 41 + 16 Reorder the terms: 16 + -8u + u2 = 41 + 16 Combine like terms: 41 + 16 = 57 16 + -8u + u2 = 57 Factor a perfect square on the left side: (u + -4)(u + -4) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (u + -4) equal to 7.549834435 and -7.549834435.Subproblem 1
u + -4 = 7.549834435 Simplifying u + -4 = 7.549834435 Reorder the terms: -4 + u = 7.549834435 Solving -4 + u = 7.549834435 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 = 7.549834435 + 4 Combine like terms: -4 + 4 = 0 0 + u = 7.549834435 + 4 u = 7.549834435 + 4 Combine like terms: 7.549834435 + 4 = 11.549834435 u = 11.549834435 Simplifying u = 11.549834435Subproblem 2
u + -4 = -7.549834435 Simplifying u + -4 = -7.549834435 Reorder the terms: -4 + u = -7.549834435 Solving -4 + u = -7.549834435 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 = -7.549834435 + 4 Combine like terms: -4 + 4 = 0 0 + u = -7.549834435 + 4 u = -7.549834435 + 4 Combine like terms: -7.549834435 + 4 = -3.549834435 u = -3.549834435 Simplifying u = -3.549834435Solution
The solution to the problem is based on the solutions from the subproblems. u = {11.549834435, -3.549834435}
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