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Simplifying u2 + -40u + 3 = 0 Reorder the terms: 3 + -40u + u2 = 0 Solving 3 + -40u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -40u + -3 + u2 = 0 + -3 Reorder the terms: 3 + -3 + -40u + u2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -40u + u2 = 0 + -3 -40u + u2 = 0 + -3 Combine like terms: 0 + -3 = -3 -40u + u2 = -3 The u term is -40u. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40u + 400 + u2 = -3 + 400 Reorder the terms: 400 + -40u + u2 = -3 + 400 Combine like terms: -3 + 400 = 397 400 + -40u + u2 = 397 Factor a perfect square on the left side: (u + -20)(u + -20) = 397 Calculate the square root of the right side: 19.924858845 Break this problem into two subproblems by setting (u + -20) equal to 19.924858845 and -19.924858845.Subproblem 1
u + -20 = 19.924858845 Simplifying u + -20 = 19.924858845 Reorder the terms: -20 + u = 19.924858845 Solving -20 + u = 19.924858845 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + u = 19.924858845 + 20 Combine like terms: -20 + 20 = 0 0 + u = 19.924858845 + 20 u = 19.924858845 + 20 Combine like terms: 19.924858845 + 20 = 39.924858845 u = 39.924858845 Simplifying u = 39.924858845Subproblem 2
u + -20 = -19.924858845 Simplifying u + -20 = -19.924858845 Reorder the terms: -20 + u = -19.924858845 Solving -20 + u = -19.924858845 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + u = -19.924858845 + 20 Combine like terms: -20 + 20 = 0 0 + u = -19.924858845 + 20 u = -19.924858845 + 20 Combine like terms: -19.924858845 + 20 = 0.075141155 u = 0.075141155 Simplifying u = 0.075141155Solution
The solution to the problem is based on the solutions from the subproblems. u = {39.924858845, 0.075141155}
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