Answer:
x = - 2, x = - [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Given
5x² + 13x + 6 = 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 = 5 × 6 = 30 and sum = + 13
The factors are + 10 and + 3
Use these factors to split the x- term
5x² + 10x + 3x + 6 = 0 ( factor the first/second and third/fourth terms )
5x(x + 2) + 3(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(5x + 3) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
5x + 3 = 0 ⇒ 5x = - 3 ⇒ x = - [tex]\frac{3}{5}[/tex]
