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Simplifying u2 + -20u + 50 = 0 Reorder the terms: 50 + -20u + u2 = 0 Solving 50 + -20u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -20u + -50 + u2 = 0 + -50 Reorder the terms: 50 + -50 + -20u + u2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -20u + u2 = 0 + -50 -20u + u2 = 0 + -50 Combine like terms: 0 + -50 = -50 -20u + u2 = -50 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 = -50 + 100 Reorder the terms: 100 + -20u + u2 = -50 + 100 Combine like terms: -50 + 100 = 50 100 + -20u + u2 = 50 Factor a perfect square on the left side: (u + -10)(u + -10) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (u + -10) equal to 7.071067812 and -7.071067812.Subproblem 1
u + -10 = 7.071067812 Simplifying u + -10 = 7.071067812 Reorder the terms: -10 + u = 7.071067812 Solving -10 + u = 7.071067812 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 = 7.071067812 + 10 Combine like terms: -10 + 10 = 0 0 + u = 7.071067812 + 10 u = 7.071067812 + 10 Combine like terms: 7.071067812 + 10 = 17.071067812 u = 17.071067812 Simplifying u = 17.071067812Subproblem 2
u + -10 = -7.071067812 Simplifying u + -10 = -7.071067812 Reorder the terms: -10 + u = -7.071067812 Solving -10 + u = -7.071067812 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 = -7.071067812 + 10 Combine like terms: -10 + 10 = 0 0 + u = -7.071067812 + 10 u = -7.071067812 + 10 Combine like terms: -7.071067812 + 10 = 2.928932188 u = 2.928932188 Simplifying u = 2.928932188Solution
The solution to the problem is based on the solutions from the subproblems. u = {17.071067812, 2.928932188}
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