7. [0/1 Points] DETAILS MY NOTES Use the Square Root Property to solve the equation. $$ \begin{array}{l} x^{2}=-36 \ x=6 \end{array} $$

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You're on the right track by attempting to use the Square Root Property to solve the equation:

$$
x^{2} = -36
$$

However, there's a crucial point to consider: **the square of any real number is always non-negative**. This means that $$ x^{2} $$ cannot be negative if we're only dealing with real numbers.

### **Real Number Consideration:**

- **No Real Solutions:** Since $$ x^{2} = -36 $$ implies that a square of a real number is negative, there are **no real solutions** to this equation.

### **Complex Number Consideration:**

If we extend our scope to include **complex numbers**, we can find solutions using the imaginary unit $$ i $$, where $$ i = \sqrt{-1} $$.

- **Applying the Square Root Property:**
  $$
  x = \pm \sqrt{-36} = \pm \sqrt{36 \times (-1)} = \pm 6i
  $$

- **Solutions:**
  $$
  x = 6i \quad \text{and} \quad x = -6i
  $$

### **Final Answer:**

- **No real solutions.**
- **Complex solutions:** $$ x = 6i $$ and $$ x = -6i $$.

Make sure to specify whether you're working within the real numbers or the complex numbers, as this changes the nature of the solutions.
There are no real solutions to the equation $$ x^{2} = -36 $$. In the complex number system, the solutions are $$ x = 6i $$ and $$ x = -6i $$.

7. [0/1 Points] DETAILS MY NOTES Use the Square Root Property to solve the equation. \[ \begin{array}{l} x^{2}=-36 \\ x=6 \end{array} \]

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