Final answer:
To find the perfect square in the given equation x² - 12x = 14, complete the square by adding 36 to both sides and simplify the equation. Factor the left side as a perfect square and take the square root of both sides to solve for x.
Step-by-step explanation:
To find the perfect square in the given equation x² - 12x = 14, we need to complete the square.
Simplify the equation by adding 36 (which is half of -12) to both sides:
x² - 12x + 36 = 14 + 36
Now, factor the left side of the equation as a perfect square:
(x - 6)² = 50
Take the square root of both sides to solve for x:
x - 6 = ±√50
x = 6 ± √50