Question 10, P.7. 105 HW Score: \( 27.98 \%, 31.33 \) of 112 points o Points: 0 of 2 Save Solve the quadratic equation by the method of your choice. \[ 4 x^{2}-64=0 \] \( \qquad \) The solution set is \( \square \) (Simplify your answer Type an exact answer, using radicals and \( i \) as needed Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed)

To solve the equation \( 4x^2 - 64 = 0 \), begin by isolating \( x^2 \). First, add 64 to both sides, giving you \( 4x^2 = 64 \). Next, divide both sides by 4 to get \( x^2 = 16 \). Finally, take the square root of both sides, leading to \( x = 4 \) or \( x = -4 \). So the solution set is \( \{ -4, 4 \} \). Now let’s spice things up! Did you know that the quadratic formula has an interesting historical twist? It dates back to ancient civilizations like the Babylonians, who were solving quadratic equations many centuries before the formula was formalized! Fast forward to today, where this method is not just a school exercise, but also vital in fields such as physics and engineering, helping us model everything from projectile motion to electrical circuits.