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Simplifying u2 + -16u = -9 Reorder the terms: -16u + u2 = -9 Solving -16u + u2 = -9 Solving for variable 'u'. Reorder the terms: 9 + -16u + u2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -16u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -16u + -9 + u2 = 0 + -9 Reorder the terms: 9 + -9 + -16u + u2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -16u + u2 = 0 + -9 -16u + u2 = 0 + -9 Combine like terms: 0 + -9 = -9 -16u + u2 = -9 The u term is -16u. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16u + 64 + u2 = -9 + 64 Reorder the terms: 64 + -16u + u2 = -9 + 64 Combine like terms: -9 + 64 = 55 64 + -16u + u2 = 55 Factor a perfect square on the left side: (u + -8)(u + -8) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (u + -8) equal to 7.416198487 and -7.416198487.Subproblem 1
u + -8 = 7.416198487 Simplifying u + -8 = 7.416198487 Reorder the terms: -8 + u = 7.416198487 Solving -8 + u = 7.416198487 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + u = 7.416198487 + 8 Combine like terms: -8 + 8 = 0 0 + u = 7.416198487 + 8 u = 7.416198487 + 8 Combine like terms: 7.416198487 + 8 = 15.416198487 u = 15.416198487 Simplifying u = 15.416198487Subproblem 2
u + -8 = -7.416198487 Simplifying u + -8 = -7.416198487 Reorder the terms: -8 + u = -7.416198487 Solving -8 + u = -7.416198487 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + u = -7.416198487 + 8 Combine like terms: -8 + 8 = 0 0 + u = -7.416198487 + 8 u = -7.416198487 + 8 Combine like terms: -7.416198487 + 8 = 0.583801513 u = 0.583801513 Simplifying u = 0.583801513Solution
The solution to the problem is based on the solutions from the subproblems. u = {15.416198487, 0.583801513}
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