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Simplifying u2 + -20u + 97 = 0 Reorder the terms: 97 + -20u + u2 = 0 Solving 97 + -20u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-97' to each side of the equation. 97 + -20u + -97 + u2 = 0 + -97 Reorder the terms: 97 + -97 + -20u + u2 = 0 + -97 Combine like terms: 97 + -97 = 0 0 + -20u + u2 = 0 + -97 -20u + u2 = 0 + -97 Combine like terms: 0 + -97 = -97 -20u + u2 = -97 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 = -97 + 100 Reorder the terms: 100 + -20u + u2 = -97 + 100 Combine like terms: -97 + 100 = 3 100 + -20u + u2 = 3 Factor a perfect square on the left side: (u + -10)(u + -10) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (u + -10) equal to 1.732050808 and -1.732050808.Subproblem 1
u + -10 = 1.732050808 Simplifying u + -10 = 1.732050808 Reorder the terms: -10 + u = 1.732050808 Solving -10 + u = 1.732050808 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 = 1.732050808 + 10 Combine like terms: -10 + 10 = 0 0 + u = 1.732050808 + 10 u = 1.732050808 + 10 Combine like terms: 1.732050808 + 10 = 11.732050808 u = 11.732050808 Simplifying u = 11.732050808Subproblem 2
u + -10 = -1.732050808 Simplifying u + -10 = -1.732050808 Reorder the terms: -10 + u = -1.732050808 Solving -10 + u = -1.732050808 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 = -1.732050808 + 10 Combine like terms: -10 + 10 = 0 0 + u = -1.732050808 + 10 u = -1.732050808 + 10 Combine like terms: -1.732050808 + 10 = 8.267949192 u = 8.267949192 Simplifying u = 8.267949192Solution
The solution to the problem is based on the solutions from the subproblems. u = {11.732050808, 8.267949192}
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