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Simplifying 3u2 + -5u + -24 = 0 Reorder the terms: -24 + -5u + 3u2 = 0 Solving -24 + -5u + 3u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + -1.666666667u + u2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -1.666666667u + 8 + u2 = 0 + 8 Reorder the terms: -8 + 8 + -1.666666667u + u2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1.666666667u + u2 = 0 + 8 -1.666666667u + u2 = 0 + 8 Combine like terms: 0 + 8 = 8 -1.666666667u + u2 = 8 The u term is -1.666666667u. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667u + 0.6944444447 + u2 = 8 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667u + u2 = 8 + 0.6944444447 Combine like terms: 8 + 0.6944444447 = 8.6944444447 0.6944444447 + -1.666666667u + u2 = 8.6944444447 Factor a perfect square on the left side: (u + -0.8333333335)(u + -0.8333333335) = 8.6944444447 Calculate the square root of the right side: 2.948634336 Break this problem into two subproblems by setting (u + -0.8333333335) equal to 2.948634336 and -2.948634336.Subproblem 1
u + -0.8333333335 = 2.948634336 Simplifying u + -0.8333333335 = 2.948634336 Reorder the terms: -0.8333333335 + u = 2.948634336 Solving -0.8333333335 + u = 2.948634336 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + u = 2.948634336 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + u = 2.948634336 + 0.8333333335 u = 2.948634336 + 0.8333333335 Combine like terms: 2.948634336 + 0.8333333335 = 3.7819676695 u = 3.7819676695 Simplifying u = 3.7819676695Subproblem 2
u + -0.8333333335 = -2.948634336 Simplifying u + -0.8333333335 = -2.948634336 Reorder the terms: -0.8333333335 + u = -2.948634336 Solving -0.8333333335 + u = -2.948634336 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + u = -2.948634336 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + u = -2.948634336 + 0.8333333335 u = -2.948634336 + 0.8333333335 Combine like terms: -2.948634336 + 0.8333333335 = -2.1153010025 u = -2.1153010025 Simplifying u = -2.1153010025Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.7819676695, -2.1153010025}
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