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Simplifying u2 + 20u + -72 = 0 Reorder the terms: -72 + 20u + u2 = 0 Solving -72 + 20u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 20u + 72 + u2 = 0 + 72 Reorder the terms: -72 + 72 + 20u + u2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 20u + u2 = 0 + 72 20u + u2 = 0 + 72 Combine like terms: 0 + 72 = 72 20u + u2 = 72 The u term is 20u. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20u + 100 + u2 = 72 + 100 Reorder the terms: 100 + 20u + u2 = 72 + 100 Combine like terms: 72 + 100 = 172 100 + 20u + u2 = 172 Factor a perfect square on the left side: (u + 10)(u + 10) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (u + 10) equal to 13.114877049 and -13.114877049.Subproblem 1
u + 10 = 13.114877049 Simplifying u + 10 = 13.114877049 Reorder the terms: 10 + u = 13.114877049 Solving 10 + u = 13.114877049 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + u = 13.114877049 + -10 Combine like terms: 10 + -10 = 0 0 + u = 13.114877049 + -10 u = 13.114877049 + -10 Combine like terms: 13.114877049 + -10 = 3.114877049 u = 3.114877049 Simplifying u = 3.114877049Subproblem 2
u + 10 = -13.114877049 Simplifying u + 10 = -13.114877049 Reorder the terms: 10 + u = -13.114877049 Solving 10 + u = -13.114877049 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + u = -13.114877049 + -10 Combine like terms: 10 + -10 = 0 0 + u = -13.114877049 + -10 u = -13.114877049 + -10 Combine like terms: -13.114877049 + -10 = -23.114877049 u = -23.114877049 Simplifying u = -23.114877049Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.114877049, -23.114877049}
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