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Simplifying (u + -4)(u + -4) = 2u2 + u + 36 Reorder the terms: (-4 + u)(u + -4) = 2u2 + u + 36 Reorder the terms: (-4 + u)(-4 + u) = 2u2 + u + 36 Multiply (-4 + u) * (-4 + u) (-4(-4 + u) + u(-4 + u)) = 2u2 + u + 36 ((-4 * -4 + u * -4) + u(-4 + u)) = 2u2 + u + 36 ((16 + -4u) + u(-4 + u)) = 2u2 + u + 36 (16 + -4u + (-4 * u + u * u)) = 2u2 + u + 36 (16 + -4u + (-4u + u2)) = 2u2 + u + 36 Combine like terms: -4u + -4u = -8u (16 + -8u + u2) = 2u2 + u + 36 Reorder the terms: 16 + -8u + u2 = 36 + u + 2u2 Solving 16 + -8u + u2 = 36 + u + 2u2 Solving for variable 'u'. Reorder the terms: 16 + -36 + -8u + -1u + u2 + -2u2 = 36 + u + 2u2 + -36 + -1u + -2u2 Combine like terms: 16 + -36 = -20 -20 + -8u + -1u + u2 + -2u2 = 36 + u + 2u2 + -36 + -1u + -2u2 Combine like terms: -8u + -1u = -9u -20 + -9u + u2 + -2u2 = 36 + u + 2u2 + -36 + -1u + -2u2 Combine like terms: u2 + -2u2 = -1u2 -20 + -9u + -1u2 = 36 + u + 2u2 + -36 + -1u + -2u2 Reorder the terms: -20 + -9u + -1u2 = 36 + -36 + u + -1u + 2u2 + -2u2 Combine like terms: 36 + -36 = 0 -20 + -9u + -1u2 = 0 + u + -1u + 2u2 + -2u2 -20 + -9u + -1u2 = u + -1u + 2u2 + -2u2 Combine like terms: u + -1u = 0 -20 + -9u + -1u2 = 0 + 2u2 + -2u2 -20 + -9u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -20 + -9u + -1u2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 9u + u2) = 0 Factor a trinomial. -1((5 + u)(4 + u)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + u)' equal to zero and attempt to solve: Simplifying 5 + u = 0 Solving 5 + u = 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 + u = 0 + -5 Combine like terms: 5 + -5 = 0 0 + u = 0 + -5 u = 0 + -5 Combine like terms: 0 + -5 = -5 u = -5 Simplifying u = -5Subproblem 2
Set the factor '(4 + u)' equal to zero and attempt to solve: Simplifying 4 + u = 0 Solving 4 + u = 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 + u = 0 + -4 Combine like terms: 4 + -4 = 0 0 + u = 0 + -4 u = 0 + -4 Combine like terms: 0 + -4 = -4 u = -4 Simplifying u = -4Solution
u = {-5, -4}
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