Answer:
x = [tex]\frac{2}{5}[/tex], x = 4
Step-by-step explanation:
Given
5x² - 22x + 8 = 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 = 5 × 8 = + 40 and sum = - 22
The factors are - 20 and - 2
Use these factors to split the x- term
5x² - 20x - 2x + 8 = 0 ( factor the first/second and third/fourth terms )
5x(x - 4) - 2(x - 4) = 0 ← factor out (x - 4) from each term
(x - 4)(5x - 2) = 0
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
5x - 2 = 0 ⇒ 5x = 2 ⇒ x = [tex]\frac{2}{5}[/tex]
