Solve: \( 16 x^{2}-81=0 \) A \( -\frac{4}{9}, \frac{4}{9} \) (B) \( -\frac{81}{16}, \frac{81}{16} \) (C) \( -\frac{16}{81}, \frac{16}{81} \) (D) \( -\frac{9}{4}, \frac{9}{4} \)

To solve the equation \( 16x^{2} - 81 = 0 \), we can first add 81 to both sides: \[ 16x^{2} = 81 \] Next, divide both sides by 16: \[ x^{2} = \frac{81}{16} \] Now, take the square root of both sides: \[ x = \pm \sqrt{\frac{81}{16}} \] \[ x = \pm \frac{9}{4} \] So the solutions are \( x = -\frac{9}{4} \) and \( x = \frac{9}{4} \). The correct answer is (D) \( -\frac{9}{4}, \frac{9}{4} \). Now, let’s dive into some interesting tidbits about this equation: Using this equation provides a clear example of the difference of squares, where we can express it in the form \( a^2 - b^2 = 0 \). This form can lead us to use the identity \( (a-b)(a+b)=0 \), which can make solving quadratic equations easier and faster! Many real-world applications of quadratic equations, like projectile motion, describe paths taken by objects in the air, such as a basketball being shot into a hoop. Using the same principles, we can calculate optimal angles and forces, ensuring spectacular shots and impressive three-pointers!