solve: $16x^2 - 81 = 0$\n\na $-\\frac{4}{9}, \\frac{4}{9}$\n\nb $-\\frac{81}{16}, \\frac{81}{16}$\n\nc…

solve: $16x^2 - 81 = 0$\n\na $-\\frac{4}{9}, \\frac{4}{9}$\n\nb $-\\frac{81}{16}, \\frac{81}{16}$\n\nc $-\\frac{16}{81}, \\frac{16}{81}$\n\nd $-\\frac{9}{4}, \\frac{9}{4}$

solve: $16x^2 - 81 = 0$\n\na $-\\frac{4}{9}, \\frac{4}{9}$\n\nb $-\\frac{81}{16}, \\frac{81}{16}$\n\nc $-\\frac{16}{81}, \\frac{16}{81}$\n\nd $-\\frac{9}{4}, \\frac{9}{4}$

Answer

Explanation:

Step1: Isolate the quadratic term

Add $81$ to both sides of the equation. $$16x^{2} = 81$$

Step2: Solve for $x^{2}$

Divide both sides by $16$. $$x^{2} = \frac{81}{16}$$

Step3: Apply the square root property

Take the square root of both sides, including both positive and negative roots. $$x = \pm \sqrt{\frac{81}{16}}$$

Step4: Simplify the square root

Calculate the square root of the numerator and the denominator. $$x = \pm \frac{9}{4}$$

Answer:

D. $-\frac{9}{4}, \frac{9}{4}$