Solve each equation using the quadratic formula.
\[ 2v^2 + 12v - 27 = 9v \]
Answer (2)
2 v 2 + 12 v − 27 = 9 v / − 9 v 2 v 2 + 3 v − 27 = 0 a = 2 ; b = 3 ; c = − 27 Δ = b 2 − 4 a c Δ = 3 2 − 4 ⋅ 2 ⋅ ( − 27 ) = 9 + 216 = 225 v 1 = 2 a − b − Δ ; v 2 = 2 a − b + Δ v 1 = 2 ⋅ 2 − 3 − 225 = 4 − 3 − 15 = 4 − 18 = − 4 2 1 v 2 = 2 ⋅ 2 − 3 + 15 = 4 12 = 3
2 v 2 + 3 v − 27 = 0 2 ( v + 4 2 1 ) ( v − 3 ) = 0 A n s w er : v = − 4 2 1 ∨ v = 3.
The solutions to the equation 2 v 2 + 12 v − 27 = 9 v are v = − 4.5 and v = 3 . These solutions were obtained by rearranging the equation into standard form and applying the quadratic formula. The discriminant was calculated to ensure the solutions were real numbers.
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