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Simplifying (u + 4)(u + 4) = 2u2 + 10u + 13 Reorder the terms: (4 + u)(u + 4) = 2u2 + 10u + 13 Reorder the terms: (4 + u)(4 + u) = 2u2 + 10u + 13 Multiply (4 + u) * (4 + u) (4(4 + u) + u(4 + u)) = 2u2 + 10u + 13 ((4 * 4 + u * 4) + u(4 + u)) = 2u2 + 10u + 13 ((16 + 4u) + u(4 + u)) = 2u2 + 10u + 13 (16 + 4u + (4 * u + u * u)) = 2u2 + 10u + 13 (16 + 4u + (4u + u2)) = 2u2 + 10u + 13 Combine like terms: 4u + 4u = 8u (16 + 8u + u2) = 2u2 + 10u + 13 Reorder the terms: 16 + 8u + u2 = 13 + 10u + 2u2 Solving 16 + 8u + u2 = 13 + 10u + 2u2 Solving for variable 'u'. Reorder the terms: 16 + -13 + 8u + -10u + u2 + -2u2 = 13 + 10u + 2u2 + -13 + -10u + -2u2 Combine like terms: 16 + -13 = 3 3 + 8u + -10u + u2 + -2u2 = 13 + 10u + 2u2 + -13 + -10u + -2u2 Combine like terms: 8u + -10u = -2u 3 + -2u + u2 + -2u2 = 13 + 10u + 2u2 + -13 + -10u + -2u2 Combine like terms: u2 + -2u2 = -1u2 3 + -2u + -1u2 = 13 + 10u + 2u2 + -13 + -10u + -2u2 Reorder the terms: 3 + -2u + -1u2 = 13 + -13 + 10u + -10u + 2u2 + -2u2 Combine like terms: 13 + -13 = 0 3 + -2u + -1u2 = 0 + 10u + -10u + 2u2 + -2u2 3 + -2u + -1u2 = 10u + -10u + 2u2 + -2u2 Combine like terms: 10u + -10u = 0 3 + -2u + -1u2 = 0 + 2u2 + -2u2 3 + -2u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 3 + -2u + -1u2 = 0 Factor a trinomial. (1 + -1u)(3 + u) = 0Subproblem 1
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 = 1Subproblem 2
Set the factor '(3 + u)' equal to zero and attempt to solve: Simplifying 3 + u = 0 Solving 3 + u = 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 + u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + u = 0 + -3 u = 0 + -3 Combine like terms: 0 + -3 = -3 u = -3 Simplifying u = -3Solution
u = {1, -3}
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