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Simplifying u2 + 28u = 11 Reorder the terms: 28u + u2 = 11 Solving 28u + u2 = 11 Solving for variable 'u'. Reorder the terms: -11 + 28u + u2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 28u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 28u + 11 + u2 = 0 + 11 Reorder the terms: -11 + 11 + 28u + u2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 28u + u2 = 0 + 11 28u + u2 = 0 + 11 Combine like terms: 0 + 11 = 11 28u + u2 = 11 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 = 11 + 196 Reorder the terms: 196 + 28u + u2 = 11 + 196 Combine like terms: 11 + 196 = 207 196 + 28u + u2 = 207 Factor a perfect square on the left side: (u + 14)(u + 14) = 207 Calculate the square root of the right side: 14.38749457 Break this problem into two subproblems by setting (u + 14) equal to 14.38749457 and -14.38749457.Subproblem 1
u + 14 = 14.38749457 Simplifying u + 14 = 14.38749457 Reorder the terms: 14 + u = 14.38749457 Solving 14 + u = 14.38749457 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 = 14.38749457 + -14 Combine like terms: 14 + -14 = 0 0 + u = 14.38749457 + -14 u = 14.38749457 + -14 Combine like terms: 14.38749457 + -14 = 0.38749457 u = 0.38749457 Simplifying u = 0.38749457Subproblem 2
u + 14 = -14.38749457 Simplifying u + 14 = -14.38749457 Reorder the terms: 14 + u = -14.38749457 Solving 14 + u = -14.38749457 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 = -14.38749457 + -14 Combine like terms: 14 + -14 = 0 0 + u = -14.38749457 + -14 u = -14.38749457 + -14 Combine like terms: -14.38749457 + -14 = -28.38749457 u = -28.38749457 Simplifying u = -28.38749457Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.38749457, -28.38749457}
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