The equation is $x^2 = -121$. To solve it using the square root property:

Steps:

1. Rewrite the equation: $x^2 = -121$

2. Take the square root of both sides. Remember that the square root of a negative number introduces an imaginary unit ($i$): $x = \pm \sqrt{-121}$

3. Simplify the square root: $\sqrt{-121} = \sqrt{121} \cdot \sqrt{-1} = 11i$

4. Therefore, the solutions are: $x = \pm 11i$

Final Answer:

The solution set is: $\{ -11i, 11i \}$

Would you like further clarification or have additional questions?

Relative Questions:

1. What is the meaning of the imaginary unit $i$?
2. How do you handle square roots of negative numbers in other equations?
3. What does it mean for a solution to be in terms of $i$?
4. Can square roots of negative numbers have real solutions?
5. How can we verify the solutions to this equation?

Tip:

Always simplify the square root of negative numbers using $i$, where $i = \sqrt{-1}$, to ensure proper solutions in the complex number system.