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Simplifying (u + -7)(u + -7) = 2u2 + -6u + 61 Reorder the terms: (-7 + u)(u + -7) = 2u2 + -6u + 61 Reorder the terms: (-7 + u)(-7 + u) = 2u2 + -6u + 61 Multiply (-7 + u) * (-7 + u) (-7(-7 + u) + u(-7 + u)) = 2u2 + -6u + 61 ((-7 * -7 + u * -7) + u(-7 + u)) = 2u2 + -6u + 61 ((49 + -7u) + u(-7 + u)) = 2u2 + -6u + 61 (49 + -7u + (-7 * u + u * u)) = 2u2 + -6u + 61 (49 + -7u + (-7u + u2)) = 2u2 + -6u + 61 Combine like terms: -7u + -7u = -14u (49 + -14u + u2) = 2u2 + -6u + 61 Reorder the terms: 49 + -14u + u2 = 61 + -6u + 2u2 Solving 49 + -14u + u2 = 61 + -6u + 2u2 Solving for variable 'u'. Reorder the terms: 49 + -61 + -14u + 6u + u2 + -2u2 = 61 + -6u + 2u2 + -61 + 6u + -2u2 Combine like terms: 49 + -61 = -12 -12 + -14u + 6u + u2 + -2u2 = 61 + -6u + 2u2 + -61 + 6u + -2u2 Combine like terms: -14u + 6u = -8u -12 + -8u + u2 + -2u2 = 61 + -6u + 2u2 + -61 + 6u + -2u2 Combine like terms: u2 + -2u2 = -1u2 -12 + -8u + -1u2 = 61 + -6u + 2u2 + -61 + 6u + -2u2 Reorder the terms: -12 + -8u + -1u2 = 61 + -61 + -6u + 6u + 2u2 + -2u2 Combine like terms: 61 + -61 = 0 -12 + -8u + -1u2 = 0 + -6u + 6u + 2u2 + -2u2 -12 + -8u + -1u2 = -6u + 6u + 2u2 + -2u2 Combine like terms: -6u + 6u = 0 -12 + -8u + -1u2 = 0 + 2u2 + -2u2 -12 + -8u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -12 + -8u + -1u2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 8u + u2) = 0 Factor a trinomial. -1((6 + u)(2 + u)) = 0 Ignore the factor -1.Subproblem 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 '(2 + u)' equal to zero and attempt to solve: Simplifying 2 + u = 0 Solving 2 + u = 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 + u = 0 + -2 Combine like terms: 2 + -2 = 0 0 + u = 0 + -2 u = 0 + -2 Combine like terms: 0 + -2 = -2 u = -2 Simplifying u = -2Solution
u = {-6, -2}
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