Final answer:
To solve the equation x² = 121, take the square root of both sides to find two solutions: x = 11 and x = -11, since both positive and negative numbers when squared will yield 121.
Step-by-step explanation:
To solve the quadratic equation by extracting the square root, we start with the equation x² = 121. Since 121 is a perfect square, we can take the square root of both sides to find that x can be either the positive or negative square root of 121. Therefore:
- √x² = √121
- x = ±√121
- x = ±11
The solutions are x = 11 or x = -11. Remember that squaring a positive or negative number gives a positive result, so both positive and negative square roots could be solutions to the original equation.