Final answer:
To solve the equation 2h² - 5 = 27 for h, add 5 to both sides, divide by 2, and then take the square root, yielding solutions h = 4 and h = -4.
Step-by-step explanation:
To solve the following equation for h: 2h² - 5 = 27, we first isolate the term with the variable on one side. Starting with 2h² - 5 = 27, we add 5 to both sides to get 2h² = 32. Next, we divide both sides by 2 to isolate h², resulting in h² = 16. Finally, we take the square root of both sides to solve for h, which gives us h = ±√16. Therefore, the solutions for h are h = 4 and h = -4.