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Simplifying u2 + -16u + 33 = 0 Reorder the terms: 33 + -16u + u2 = 0 Solving 33 + -16u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + -16u + -33 + u2 = 0 + -33 Reorder the terms: 33 + -33 + -16u + u2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -16u + u2 = 0 + -33 -16u + u2 = 0 + -33 Combine like terms: 0 + -33 = -33 -16u + u2 = -33 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 = -33 + 64 Reorder the terms: 64 + -16u + u2 = -33 + 64 Combine like terms: -33 + 64 = 31 64 + -16u + u2 = 31 Factor a perfect square on the left side: (u + -8)(u + -8) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (u + -8) equal to 5.567764363 and -5.567764363.Subproblem 1
u + -8 = 5.567764363 Simplifying u + -8 = 5.567764363 Reorder the terms: -8 + u = 5.567764363 Solving -8 + u = 5.567764363 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 = 5.567764363 + 8 Combine like terms: -8 + 8 = 0 0 + u = 5.567764363 + 8 u = 5.567764363 + 8 Combine like terms: 5.567764363 + 8 = 13.567764363 u = 13.567764363 Simplifying u = 13.567764363Subproblem 2
u + -8 = -5.567764363 Simplifying u + -8 = -5.567764363 Reorder the terms: -8 + u = -5.567764363 Solving -8 + u = -5.567764363 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 = -5.567764363 + 8 Combine like terms: -8 + 8 = 0 0 + u = -5.567764363 + 8 u = -5.567764363 + 8 Combine like terms: -5.567764363 + 8 = 2.432235637 u = 2.432235637 Simplifying u = 2.432235637Solution
The solution to the problem is based on the solutions from the subproblems. u = {13.567764363, 2.432235637}
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