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Simplifying -3u2 + 48u + -81 = 0 Reorder the terms: -81 + 48u + -3u2 = 0 Solving -81 + 48u + -3u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '3'. 3(-27 + 16u + -1u2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-27 + 16u + -1u2)' equal to zero and attempt to solve: Simplifying -27 + 16u + -1u2 = 0 Solving -27 + 16u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 27 + -16u + u2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -16u + -27 + u2 = 0 + -27 Reorder the terms: 27 + -27 + -16u + u2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -16u + u2 = 0 + -27 -16u + u2 = 0 + -27 Combine like terms: 0 + -27 = -27 -16u + u2 = -27 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 = -27 + 64 Reorder the terms: 64 + -16u + u2 = -27 + 64 Combine like terms: -27 + 64 = 37 64 + -16u + u2 = 37 Factor a perfect square on the left side: (u + -8)(u + -8) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (u + -8) equal to 6.08276253 and -6.08276253.Subproblem 1
u + -8 = 6.08276253 Simplifying u + -8 = 6.08276253 Reorder the terms: -8 + u = 6.08276253 Solving -8 + u = 6.08276253 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 = 6.08276253 + 8 Combine like terms: -8 + 8 = 0 0 + u = 6.08276253 + 8 u = 6.08276253 + 8 Combine like terms: 6.08276253 + 8 = 14.08276253 u = 14.08276253 Simplifying u = 14.08276253Subproblem 2
u + -8 = -6.08276253 Simplifying u + -8 = -6.08276253 Reorder the terms: -8 + u = -6.08276253 Solving -8 + u = -6.08276253 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 = -6.08276253 + 8 Combine like terms: -8 + 8 = 0 0 + u = -6.08276253 + 8 u = -6.08276253 + 8 Combine like terms: -6.08276253 + 8 = 1.91723747 u = 1.91723747 Simplifying u = 1.91723747Solution
The solution to the problem is based on the solutions from the subproblems. u = {14.08276253, 1.91723747}Solution
u = {14.08276253, 1.91723747}
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