Question

Solve the equation with special factors. (Please show all steps)
16q^2 - 81 = 0

Answer 1

Answer:
`q=(√(81))/(16)`

Explanation:

`16q^2-81=0\\16q^2=0+81=81\\16q=√(81) \\q=(√(81))/(16)`

Answer 2

q = ±
`(9)/(4)`

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 =
`(9)/(4)`

4q + 9 = 0 ⇒ 4q = - 9 ⇒ q = -
`(9)/(4)`