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Simplifying 0 = 3u2 + 16u + -30 Reorder the terms: 0 = -30 + 16u + 3u2 Solving 0 = -30 + 16u + 3u2 Solving for variable 'u'. Combine like terms: 0 + 30 = 30 30 + -16u + -3u2 = -30 + 16u + 3u2 + 30 + -16u + -3u2 Reorder the terms: 30 + -16u + -3u2 = -30 + 30 + 16u + -16u + 3u2 + -3u2 Combine like terms: -30 + 30 = 0 30 + -16u + -3u2 = 0 + 16u + -16u + 3u2 + -3u2 30 + -16u + -3u2 = 16u + -16u + 3u2 + -3u2 Combine like terms: 16u + -16u = 0 30 + -16u + -3u2 = 0 + 3u2 + -3u2 30 + -16u + -3u2 = 3u2 + -3u2 Combine like terms: 3u2 + -3u2 = 0 30 + -16u + -3u2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -10 + 5.333333333u + u2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 5.333333333u + 10 + u2 = 0 + 10 Reorder the terms: -10 + 10 + 5.333333333u + u2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 5.333333333u + u2 = 0 + 10 5.333333333u + u2 = 0 + 10 Combine like terms: 0 + 10 = 10 5.333333333u + u2 = 10 The u term is 5.333333333u. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333u + 7.111111113 + u2 = 10 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333u + u2 = 10 + 7.111111113 Combine like terms: 10 + 7.111111113 = 17.111111113 7.111111113 + 5.333333333u + u2 = 17.111111113 Factor a perfect square on the left side: (u + 2.666666667)(u + 2.666666667) = 17.111111113 Calculate the square root of the right side: 4.136557882 Break this problem into two subproblems by setting (u + 2.666666667) equal to 4.136557882 and -4.136557882.Subproblem 1
u + 2.666666667 = 4.136557882 Simplifying u + 2.666666667 = 4.136557882 Reorder the terms: 2.666666667 + u = 4.136557882 Solving 2.666666667 + u = 4.136557882 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + u = 4.136557882 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + u = 4.136557882 + -2.666666667 u = 4.136557882 + -2.666666667 Combine like terms: 4.136557882 + -2.666666667 = 1.469891215 u = 1.469891215 Simplifying u = 1.469891215Subproblem 2
u + 2.666666667 = -4.136557882 Simplifying u + 2.666666667 = -4.136557882 Reorder the terms: 2.666666667 + u = -4.136557882 Solving 2.666666667 + u = -4.136557882 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + u = -4.136557882 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + u = -4.136557882 + -2.666666667 u = -4.136557882 + -2.666666667 Combine like terms: -4.136557882 + -2.666666667 = -6.803224549 u = -6.803224549 Simplifying u = -6.803224549Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.469891215, -6.803224549}
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