Answer:
x = - [tex]\frac{1}{2}[/tex], x = 3
Step-by-step explanation:
Given
2x² - 5x - 3 = 0 ← in standard form
Consider the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 3 = - 6 and sum = - 5
The factors are - 6 and + 1
Use these factors to split the x- term
2x² - 6x + x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(x - 3) + 1 (x - 3) = 0 ← factor out (x - 3) from each term
(x - 3)(2x + 1) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
x - 3 = 0 ⇒ x = 3
