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Simplifying u2 + -22u = 15 Reorder the terms: -22u + u2 = 15 Solving -22u + u2 = 15 Solving for variable 'u'. Reorder the terms: -15 + -22u + u2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -22u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -22u + 15 + u2 = 0 + 15 Reorder the terms: -15 + 15 + -22u + u2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -22u + u2 = 0 + 15 -22u + u2 = 0 + 15 Combine like terms: 0 + 15 = 15 -22u + u2 = 15 The u term is -22u. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22u + 121 + u2 = 15 + 121 Reorder the terms: 121 + -22u + u2 = 15 + 121 Combine like terms: 15 + 121 = 136 121 + -22u + u2 = 136 Factor a perfect square on the left side: (u + -11)(u + -11) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (u + -11) equal to 11.66190379 and -11.66190379.Subproblem 1
u + -11 = 11.66190379 Simplifying u + -11 = 11.66190379 Reorder the terms: -11 + u = 11.66190379 Solving -11 + u = 11.66190379 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + u = 11.66190379 + 11 Combine like terms: -11 + 11 = 0 0 + u = 11.66190379 + 11 u = 11.66190379 + 11 Combine like terms: 11.66190379 + 11 = 22.66190379 u = 22.66190379 Simplifying u = 22.66190379Subproblem 2
u + -11 = -11.66190379 Simplifying u + -11 = -11.66190379 Reorder the terms: -11 + u = -11.66190379 Solving -11 + u = -11.66190379 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + u = -11.66190379 + 11 Combine like terms: -11 + 11 = 0 0 + u = -11.66190379 + 11 u = -11.66190379 + 11 Combine like terms: -11.66190379 + 11 = -0.66190379 u = -0.66190379 Simplifying u = -0.66190379Solution
The solution to the problem is based on the solutions from the subproblems. u = {22.66190379, -0.66190379}
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