Answer:
x = - 1, x = [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Given
9x² + 4x - 5 = 0
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 9 × - 5 = - 45 and sum = + 4
the factors are + 9 and - 5
Use these factors to split the x- term
9x² + 9x - 5x - 5 = 0 ( factor the first/second and third/fourth terms )
9x(x + 1) - 5(x + 1) = 0 ← factor out (x + 1) from each term
(x + 1)(9x - 5) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
9x - 5 = 0 ⇒ 9x = 5 ⇒ x = [tex]\frac{5}{9}[/tex]
