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Simplifying (u + 7)(u + 7) = 2u2 + 3u + 79 Reorder the terms: (7 + u)(u + 7) = 2u2 + 3u + 79 Reorder the terms: (7 + u)(7 + u) = 2u2 + 3u + 79 Multiply (7 + u) * (7 + u) (7(7 + u) + u(7 + u)) = 2u2 + 3u + 79 ((7 * 7 + u * 7) + u(7 + u)) = 2u2 + 3u + 79 ((49 + 7u) + u(7 + u)) = 2u2 + 3u + 79 (49 + 7u + (7 * u + u * u)) = 2u2 + 3u + 79 (49 + 7u + (7u + u2)) = 2u2 + 3u + 79 Combine like terms: 7u + 7u = 14u (49 + 14u + u2) = 2u2 + 3u + 79 Reorder the terms: 49 + 14u + u2 = 79 + 3u + 2u2 Solving 49 + 14u + u2 = 79 + 3u + 2u2 Solving for variable 'u'. Reorder the terms: 49 + -79 + 14u + -3u + u2 + -2u2 = 79 + 3u + 2u2 + -79 + -3u + -2u2 Combine like terms: 49 + -79 = -30 -30 + 14u + -3u + u2 + -2u2 = 79 + 3u + 2u2 + -79 + -3u + -2u2 Combine like terms: 14u + -3u = 11u -30 + 11u + u2 + -2u2 = 79 + 3u + 2u2 + -79 + -3u + -2u2 Combine like terms: u2 + -2u2 = -1u2 -30 + 11u + -1u2 = 79 + 3u + 2u2 + -79 + -3u + -2u2 Reorder the terms: -30 + 11u + -1u2 = 79 + -79 + 3u + -3u + 2u2 + -2u2 Combine like terms: 79 + -79 = 0 -30 + 11u + -1u2 = 0 + 3u + -3u + 2u2 + -2u2 -30 + 11u + -1u2 = 3u + -3u + 2u2 + -2u2 Combine like terms: 3u + -3u = 0 -30 + 11u + -1u2 = 0 + 2u2 + -2u2 -30 + 11u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -30 + 11u + -1u2 = 0 Factor a trinomial. (-6 + u)(5 + -1u) = 0Subproblem 1
Set the factor '(-6 + u)' equal to zero and attempt to solve: Simplifying -6 + u = 0 Solving -6 + u = 0 Move all terms containing u to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + u = 0 + 6 Combine like terms: -6 + 6 = 0 0 + u = 0 + 6 u = 0 + 6 Combine like terms: 0 + 6 = 6 u = 6 Simplifying u = 6Subproblem 2
Set the factor '(5 + -1u)' equal to zero and attempt to solve: Simplifying 5 + -1u = 0 Solving 5 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1u = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1u = 0 + -5 -1u = 0 + -5 Combine like terms: 0 + -5 = -5 -1u = -5 Divide each side by '-1'. u = 5 Simplifying u = 5Solution
u = {6, 5}
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