Answer:
x = - [tex]\frac{1}{4}[/tex], x = 2
Step-by-step explanation:
Given
4x² - 7x - 2 = 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 = 4 × - 2 = - 8 and sum = - 7
The factors are - 8 and + 1
Use these factors to split the x- term
4x² - 8x + x - 2 = 0 ( factor the first/second and third/fourth terms )
4x(x - 2) + 1(x - 2) = 0 ← factor out (x - 2) from each term
(x - 2)(4x + 1) = 0
Equate each factor to zero and solve for x
4x + 1 = 0 ⇒ 4x = - 1 ⇒ x = - [tex]\frac{1}{4}[/tex]
x - 2 = 0 ⇒ x = 2
