Answer:
q = ± [tex]\frac{9}{4}[/tex]
Step-by-step explanation:
16q² - 81 = 0 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
16q² - 81 = 0
(4q)² - 9² = 0
(4q - 9)(4q + 9) = 0
Equate each factor to zero and solve for q
4q - 9 = 0 ⇒ 4q = 9 ⇒ q = [tex]\frac{9}{4}[/tex]
4q + 9 = 0 ⇒ 4q = - 9 ⇒ q = - [tex]\frac{9}{4}[/tex]
