Question

Solve for x: 2x ^ 3 - x ^ 2 + 18x - 9 = 0

Answer 1

see explanation

Explanation:

Given

2x³ - x² + 18x - 9 = 0 ( factor the first/second and third/fourth terms )

x²(2x - 1) + 9(2x - 1) = 0 ← factor out (2x - 1) from each term

(2x - 1)(x² + 9) = 0

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x =
`(1)/(2)`

x² + 9 = 0 ⇒ x² = - 9 ⇒ x = ± 3i

The equation has 1 real solution and 2 complex solutions

x =
`(1)/(2)` ← real solution

x = ± 3i ← complex solutions