Answer:
x = - 3, x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given
2x² + 3x - 9 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 9 = - 18 and sum = + 3
The factors are + 6 and - 3
Use these factors to split the x- term
2x² + 6x - 3x - 9 = 0 ( factor the first/second and third/fourth terms )
2x(x + 3) - 3(x + 3) = 0 ← factor out (x + 3) from each term
(x + 3)(2x - 3) = 0
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]
