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Simplifying (u + 5)(u + 5) = 2u2 + u + 43 Reorder the terms: (5 + u)(u + 5) = 2u2 + u + 43 Reorder the terms: (5 + u)(5 + u) = 2u2 + u + 43 Multiply (5 + u) * (5 + u) (5(5 + u) + u(5 + u)) = 2u2 + u + 43 ((5 * 5 + u * 5) + u(5 + u)) = 2u2 + u + 43 ((25 + 5u) + u(5 + u)) = 2u2 + u + 43 (25 + 5u + (5 * u + u * u)) = 2u2 + u + 43 (25 + 5u + (5u + u2)) = 2u2 + u + 43 Combine like terms: 5u + 5u = 10u (25 + 10u + u2) = 2u2 + u + 43 Reorder the terms: 25 + 10u + u2 = 43 + u + 2u2 Solving 25 + 10u + u2 = 43 + u + 2u2 Solving for variable 'u'. Reorder the terms: 25 + -43 + 10u + -1u + u2 + -2u2 = 43 + u + 2u2 + -43 + -1u + -2u2 Combine like terms: 25 + -43 = -18 -18 + 10u + -1u + u2 + -2u2 = 43 + u + 2u2 + -43 + -1u + -2u2 Combine like terms: 10u + -1u = 9u -18 + 9u + u2 + -2u2 = 43 + u + 2u2 + -43 + -1u + -2u2 Combine like terms: u2 + -2u2 = -1u2 -18 + 9u + -1u2 = 43 + u + 2u2 + -43 + -1u + -2u2 Reorder the terms: -18 + 9u + -1u2 = 43 + -43 + u + -1u + 2u2 + -2u2 Combine like terms: 43 + -43 = 0 -18 + 9u + -1u2 = 0 + u + -1u + 2u2 + -2u2 -18 + 9u + -1u2 = u + -1u + 2u2 + -2u2 Combine like terms: u + -1u = 0 -18 + 9u + -1u2 = 0 + 2u2 + -2u2 -18 + 9u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -18 + 9u + -1u2 = 0 Factor a trinomial. (-6 + u)(3 + -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 '(3 + -1u)' equal to zero and attempt to solve: Simplifying 3 + -1u = 0 Solving 3 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1u = 0 + -3 -1u = 0 + -3 Combine like terms: 0 + -3 = -3 -1u = -3 Divide each side by '-1'. u = 3 Simplifying u = 3Solution
u = {6, 3}
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