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Simplifying 2u2 + 9u + 14 = u2 + 8u + 16 Reorder the terms: 14 + 9u + 2u2 = u2 + 8u + 16 Reorder the terms: 14 + 9u + 2u2 = 16 + 8u + u2 Solving 14 + 9u + 2u2 = 16 + 8u + u2 Solving for variable 'u'. Reorder the terms: 14 + -16 + 9u + -8u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2 Combine like terms: 14 + -16 = -2 -2 + 9u + -8u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2 Combine like terms: 9u + -8u = 1u -2 + 1u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2 Combine like terms: 2u2 + -1u2 = 1u2 -2 + 1u + 1u2 = 16 + 8u + u2 + -16 + -8u + -1u2 Reorder the terms: -2 + 1u + 1u2 = 16 + -16 + 8u + -8u + u2 + -1u2 Combine like terms: 16 + -16 = 0 -2 + 1u + 1u2 = 0 + 8u + -8u + u2 + -1u2 -2 + 1u + 1u2 = 8u + -8u + u2 + -1u2 Combine like terms: 8u + -8u = 0 -2 + 1u + 1u2 = 0 + u2 + -1u2 -2 + 1u + 1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 -2 + 1u + 1u2 = 0 Factor a trinomial. (-2 + -1u)(1 + -1u) = 0Subproblem 1
Set the factor '(-2 + -1u)' equal to zero and attempt to solve: Simplifying -2 + -1u = 0 Solving -2 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1u = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1u = 0 + 2 -1u = 0 + 2 Combine like terms: 0 + 2 = 2 -1u = 2 Divide each side by '-1'. u = -2 Simplifying u = -2Subproblem 2
Set the factor '(1 + -1u)' equal to zero and attempt to solve: Simplifying 1 + -1u = 0 Solving 1 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1u = 0 + -1 -1u = 0 + -1 Combine like terms: 0 + -1 = -1 -1u = -1 Divide each side by '-1'. u = 1 Simplifying u = 1Solution
u = {-2, 1}
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