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Simplifying u2 + 18u = -71 Reorder the terms: 18u + u2 = -71 Solving 18u + u2 = -71 Solving for variable 'u'. Reorder the terms: 71 + 18u + u2 = -71 + 71 Combine like terms: -71 + 71 = 0 71 + 18u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-71' to each side of the equation. 71 + 18u + -71 + u2 = 0 + -71 Reorder the terms: 71 + -71 + 18u + u2 = 0 + -71 Combine like terms: 71 + -71 = 0 0 + 18u + u2 = 0 + -71 18u + u2 = 0 + -71 Combine like terms: 0 + -71 = -71 18u + u2 = -71 The u term is 18u. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18u + 81 + u2 = -71 + 81 Reorder the terms: 81 + 18u + u2 = -71 + 81 Combine like terms: -71 + 81 = 10 81 + 18u + u2 = 10 Factor a perfect square on the left side: (u + 9)(u + 9) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (u + 9) equal to 3.16227766 and -3.16227766.Subproblem 1
u + 9 = 3.16227766 Simplifying u + 9 = 3.16227766 Reorder the terms: 9 + u = 3.16227766 Solving 9 + u = 3.16227766 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + u = 3.16227766 + -9 Combine like terms: 9 + -9 = 0 0 + u = 3.16227766 + -9 u = 3.16227766 + -9 Combine like terms: 3.16227766 + -9 = -5.83772234 u = -5.83772234 Simplifying u = -5.83772234Subproblem 2
u + 9 = -3.16227766 Simplifying u + 9 = -3.16227766 Reorder the terms: 9 + u = -3.16227766 Solving 9 + u = -3.16227766 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + u = -3.16227766 + -9 Combine like terms: 9 + -9 = 0 0 + u = -3.16227766 + -9 u = -3.16227766 + -9 Combine like terms: -3.16227766 + -9 = -12.16227766 u = -12.16227766 Simplifying u = -12.16227766Solution
The solution to the problem is based on the solutions from the subproblems. u = {-5.83772234, -12.16227766}
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