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Simplifying 2u2 + 9u + -19 = (u + 3)(u + 3) Reorder the terms: -19 + 9u + 2u2 = (u + 3)(u + 3) Reorder the terms: -19 + 9u + 2u2 = (3 + u)(u + 3) Reorder the terms: -19 + 9u + 2u2 = (3 + u)(3 + u) Multiply (3 + u) * (3 + u) -19 + 9u + 2u2 = (3(3 + u) + u(3 + u)) -19 + 9u + 2u2 = ((3 * 3 + u * 3) + u(3 + u)) -19 + 9u + 2u2 = ((9 + 3u) + u(3 + u)) -19 + 9u + 2u2 = (9 + 3u + (3 * u + u * u)) -19 + 9u + 2u2 = (9 + 3u + (3u + u2)) Combine like terms: 3u + 3u = 6u -19 + 9u + 2u2 = (9 + 6u + u2) Solving -19 + 9u + 2u2 = 9 + 6u + u2 Solving for variable 'u'. Reorder the terms: -19 + -9 + 9u + -6u + 2u2 + -1u2 = 9 + 6u + u2 + -9 + -6u + -1u2 Combine like terms: -19 + -9 = -28 -28 + 9u + -6u + 2u2 + -1u2 = 9 + 6u + u2 + -9 + -6u + -1u2 Combine like terms: 9u + -6u = 3u -28 + 3u + 2u2 + -1u2 = 9 + 6u + u2 + -9 + -6u + -1u2 Combine like terms: 2u2 + -1u2 = 1u2 -28 + 3u + 1u2 = 9 + 6u + u2 + -9 + -6u + -1u2 Reorder the terms: -28 + 3u + 1u2 = 9 + -9 + 6u + -6u + u2 + -1u2 Combine like terms: 9 + -9 = 0 -28 + 3u + 1u2 = 0 + 6u + -6u + u2 + -1u2 -28 + 3u + 1u2 = 6u + -6u + u2 + -1u2 Combine like terms: 6u + -6u = 0 -28 + 3u + 1u2 = 0 + u2 + -1u2 -28 + 3u + 1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 -28 + 3u + 1u2 = 0 Factor a trinomial. (-7 + -1u)(4 + -1u) = 0Subproblem 1
Set the factor '(-7 + -1u)' equal to zero and attempt to solve: Simplifying -7 + -1u = 0 Solving -7 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1u = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1u = 0 + 7 -1u = 0 + 7 Combine like terms: 0 + 7 = 7 -1u = 7 Divide each side by '-1'. u = -7 Simplifying u = -7Subproblem 2
Set the factor '(4 + -1u)' equal to zero and attempt to solve: Simplifying 4 + -1u = 0 Solving 4 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1u = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1u = 0 + -4 -1u = 0 + -4 Combine like terms: 0 + -4 = -4 -1u = -4 Divide each side by '-1'. u = 4 Simplifying u = 4Solution
u = {-7, 4}
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