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Simplifying 5u2 + 48u + -27 = 0 Reorder the terms: -27 + 48u + 5u2 = 0 Solving -27 + 48u + 5u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.4 + 9.6u + u2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 9.6u + 5.4 + u2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 9.6u + u2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 9.6u + u2 = 0 + 5.4 9.6u + u2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 9.6u + u2 = 5.4 The u term is 9.6u. Take half its coefficient (4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. 9.6u + 23.04 + u2 = 5.4 + 23.04 Reorder the terms: 23.04 + 9.6u + u2 = 5.4 + 23.04 Combine like terms: 5.4 + 23.04 = 28.44 23.04 + 9.6u + u2 = 28.44 Factor a perfect square on the left side: (u + 4.8)(u + 4.8) = 28.44 Calculate the square root of the right side: 5.33291665 Break this problem into two subproblems by setting (u + 4.8) equal to 5.33291665 and -5.33291665.Subproblem 1
u + 4.8 = 5.33291665 Simplifying u + 4.8 = 5.33291665 Reorder the terms: 4.8 + u = 5.33291665 Solving 4.8 + u = 5.33291665 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.8' to each side of the equation. 4.8 + -4.8 + u = 5.33291665 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + u = 5.33291665 + -4.8 u = 5.33291665 + -4.8 Combine like terms: 5.33291665 + -4.8 = 0.53291665 u = 0.53291665 Simplifying u = 0.53291665Subproblem 2
u + 4.8 = -5.33291665 Simplifying u + 4.8 = -5.33291665 Reorder the terms: 4.8 + u = -5.33291665 Solving 4.8 + u = -5.33291665 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.8' to each side of the equation. 4.8 + -4.8 + u = -5.33291665 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + u = -5.33291665 + -4.8 u = -5.33291665 + -4.8 Combine like terms: -5.33291665 + -4.8 = -10.13291665 u = -10.13291665 Simplifying u = -10.13291665Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.53291665, -10.13291665}
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