Question

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

Answer 1

Answer:

q = ± $\frac{9}{4}$

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 = $\frac{9}{4}$

4q + 9 = 0 ⇒ 4q = - 9 ⇒ q = - $\frac{9}{4}$

Answer 2

Answer: $q=\frac{\sqrt{81}}{16}$

Step-by-step explanation:

$16q^2-81=0\\16q^2=0+81=81\\16q=\sqrt{81} \\q=\frac{\sqrt{81}}{16}$