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Simplifying u2 + 28u = 31 Reorder the terms: 28u + u2 = 31 Solving 28u + u2 = 31 Solving for variable 'u'. Reorder the terms: -31 + 28u + u2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + 28u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 28u + 31 + u2 = 0 + 31 Reorder the terms: -31 + 31 + 28u + u2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 28u + u2 = 0 + 31 28u + u2 = 0 + 31 Combine like terms: 0 + 31 = 31 28u + u2 = 31 The u term is 28u. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28u + 196 + u2 = 31 + 196 Reorder the terms: 196 + 28u + u2 = 31 + 196 Combine like terms: 31 + 196 = 227 196 + 28u + u2 = 227 Factor a perfect square on the left side: (u + 14)(u + 14) = 227 Calculate the square root of the right side: 15.066519173 Break this problem into two subproblems by setting (u + 14) equal to 15.066519173 and -15.066519173.Subproblem 1
u + 14 = 15.066519173 Simplifying u + 14 = 15.066519173 Reorder the terms: 14 + u = 15.066519173 Solving 14 + u = 15.066519173 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + u = 15.066519173 + -14 Combine like terms: 14 + -14 = 0 0 + u = 15.066519173 + -14 u = 15.066519173 + -14 Combine like terms: 15.066519173 + -14 = 1.066519173 u = 1.066519173 Simplifying u = 1.066519173Subproblem 2
u + 14 = -15.066519173 Simplifying u + 14 = -15.066519173 Reorder the terms: 14 + u = -15.066519173 Solving 14 + u = -15.066519173 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + u = -15.066519173 + -14 Combine like terms: 14 + -14 = 0 0 + u = -15.066519173 + -14 u = -15.066519173 + -14 Combine like terms: -15.066519173 + -14 = -29.066519173 u = -29.066519173 Simplifying u = -29.066519173Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.066519173, -29.066519173}
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