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Simplifying u2 + 12u = 1 Reorder the terms: 12u + u2 = 1 Solving 12u + u2 = 1 Solving for variable 'u'. Reorder the terms: -1 + 12u + u2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 12u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 12u + 1 + u2 = 0 + 1 Reorder the terms: -1 + 1 + 12u + u2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 12u + u2 = 0 + 1 12u + u2 = 0 + 1 Combine like terms: 0 + 1 = 1 12u + u2 = 1 The u term is 12u. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12u + 36 + u2 = 1 + 36 Reorder the terms: 36 + 12u + u2 = 1 + 36 Combine like terms: 1 + 36 = 37 36 + 12u + u2 = 37 Factor a perfect square on the left side: (u + 6)(u + 6) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (u + 6) equal to 6.08276253 and -6.08276253.Subproblem 1
u + 6 = 6.08276253 Simplifying u + 6 = 6.08276253 Reorder the terms: 6 + u = 6.08276253 Solving 6 + u = 6.08276253 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + u = 6.08276253 + -6 Combine like terms: 6 + -6 = 0 0 + u = 6.08276253 + -6 u = 6.08276253 + -6 Combine like terms: 6.08276253 + -6 = 0.08276253 u = 0.08276253 Simplifying u = 0.08276253Subproblem 2
u + 6 = -6.08276253 Simplifying u + 6 = -6.08276253 Reorder the terms: 6 + u = -6.08276253 Solving 6 + u = -6.08276253 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + u = -6.08276253 + -6 Combine like terms: 6 + -6 = 0 0 + u = -6.08276253 + -6 u = -6.08276253 + -6 Combine like terms: -6.08276253 + -6 = -12.08276253 u = -12.08276253 Simplifying u = -12.08276253Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.08276253, -12.08276253}
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