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Simplifying u2 + -28u + 24 = 0 Reorder the terms: 24 + -28u + u2 = 0 Solving 24 + -28u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -28u + -24 + u2 = 0 + -24 Reorder the terms: 24 + -24 + -28u + u2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -28u + u2 = 0 + -24 -28u + u2 = 0 + -24 Combine like terms: 0 + -24 = -24 -28u + u2 = -24 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 = -24 + 196 Reorder the terms: 196 + -28u + u2 = -24 + 196 Combine like terms: -24 + 196 = 172 196 + -28u + u2 = 172 Factor a perfect square on the left side: (u + -14)(u + -14) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (u + -14) equal to 13.114877049 and -13.114877049.Subproblem 1
u + -14 = 13.114877049 Simplifying u + -14 = 13.114877049 Reorder the terms: -14 + u = 13.114877049 Solving -14 + u = 13.114877049 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 = 13.114877049 + 14 Combine like terms: -14 + 14 = 0 0 + u = 13.114877049 + 14 u = 13.114877049 + 14 Combine like terms: 13.114877049 + 14 = 27.114877049 u = 27.114877049 Simplifying u = 27.114877049Subproblem 2
u + -14 = -13.114877049 Simplifying u + -14 = -13.114877049 Reorder the terms: -14 + u = -13.114877049 Solving -14 + u = -13.114877049 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 = -13.114877049 + 14 Combine like terms: -14 + 14 = 0 0 + u = -13.114877049 + 14 u = -13.114877049 + 14 Combine like terms: -13.114877049 + 14 = 0.885122951 u = 0.885122951 Simplifying u = 0.885122951Solution
The solution to the problem is based on the solutions from the subproblems. u = {27.114877049, 0.885122951}
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