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Simplifying u2 + 6u = 37 Reorder the terms: 6u + u2 = 37 Solving 6u + u2 = 37 Solving for variable 'u'. Reorder the terms: -37 + 6u + u2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + 6u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 6u + 37 + u2 = 0 + 37 Reorder the terms: -37 + 37 + 6u + u2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 6u + u2 = 0 + 37 6u + u2 = 0 + 37 Combine like terms: 0 + 37 = 37 6u + u2 = 37 The u term is 6u. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6u + 9 + u2 = 37 + 9 Reorder the terms: 9 + 6u + u2 = 37 + 9 Combine like terms: 37 + 9 = 46 9 + 6u + u2 = 46 Factor a perfect square on the left side: (u + 3)(u + 3) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (u + 3) equal to 6.782329983 and -6.782329983.Subproblem 1
u + 3 = 6.782329983 Simplifying u + 3 = 6.782329983 Reorder the terms: 3 + u = 6.782329983 Solving 3 + u = 6.782329983 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = 6.782329983 + -3 Combine like terms: 3 + -3 = 0 0 + u = 6.782329983 + -3 u = 6.782329983 + -3 Combine like terms: 6.782329983 + -3 = 3.782329983 u = 3.782329983 Simplifying u = 3.782329983Subproblem 2
u + 3 = -6.782329983 Simplifying u + 3 = -6.782329983 Reorder the terms: 3 + u = -6.782329983 Solving 3 + u = -6.782329983 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = -6.782329983 + -3 Combine like terms: 3 + -3 = 0 0 + u = -6.782329983 + -3 u = -6.782329983 + -3 Combine like terms: -6.782329983 + -3 = -9.782329983 u = -9.782329983 Simplifying u = -9.782329983Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.782329983, -9.782329983}
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