Final answer:
To solve the equation (x²-4)/2 = -74 by taking square roots, we isolate x², take the square root of both sides, and find that x equals 12i and -12i.
Step-by-step explanation:
The question provided involves solving a quadratic equation by taking square roots. The given equation is (x²-4)/2 = -74. To solve it, we can first multiply both sides of the equation by 2 to get rid of the denominator, resulting in x² - 4 = -148. Next, we add 4 to both sides to isolate the x² term, resulting in x² = -144. Now, we can take the square root of both sides, remembering to include both the positive and negative solutions. Therefore, x = ±√-144, which means x is equal to 12i and -12i, where i is the imaginary unit.