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Simplifying u2 + u + -36 = 0 Reorder the terms: -36 + u + u2 = 0 Solving -36 + u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + u + 36 + u2 = 0 + 36 Reorder the terms: -36 + 36 + u + u2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + u + u2 = 0 + 36 u + u2 = 0 + 36 Combine like terms: 0 + 36 = 36 u + u2 = 36 The u term is u. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. u + 0.25 + u2 = 36 + 0.25 Reorder the terms: 0.25 + u + u2 = 36 + 0.25 Combine like terms: 36 + 0.25 = 36.25 0.25 + u + u2 = 36.25 Factor a perfect square on the left side: (u + 0.5)(u + 0.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (u + 0.5) equal to 6.020797289 and -6.020797289.Subproblem 1
u + 0.5 = 6.020797289 Simplifying u + 0.5 = 6.020797289 Reorder the terms: 0.5 + u = 6.020797289 Solving 0.5 + u = 6.020797289 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + u = 6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = 6.020797289 + -0.5 u = 6.020797289 + -0.5 Combine like terms: 6.020797289 + -0.5 = 5.520797289 u = 5.520797289 Simplifying u = 5.520797289Subproblem 2
u + 0.5 = -6.020797289 Simplifying u + 0.5 = -6.020797289 Reorder the terms: 0.5 + u = -6.020797289 Solving 0.5 + u = -6.020797289 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + u = -6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = -6.020797289 + -0.5 u = -6.020797289 + -0.5 Combine like terms: -6.020797289 + -0.5 = -6.520797289 u = -6.520797289 Simplifying u = -6.520797289Solution
The solution to the problem is based on the solutions from the subproblems. u = {5.520797289, -6.520797289}
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