https://file.aiquickdraw.com/mathbot/file/17271979360585mqmrsy8.jpg

Let's solve the given equation step by step:

The equation is:
\[
h^2 - 13 = -4
\]

### Step 1: Move constants to one side
Add 13 to both sides to isolate \( h^2 \) on the left side:
\[
h^2 = -4 + 13
\]
\[
h^2 = 9
\]

### Step 2: Solve for \( h \)
Now take the square root of both sides:
\[
h = \pm \sqrt{9}
\]
\[
h = \pm 3
\]

### Final Answer:
The solutions for \( h \) are:
\[
h = 3 \quad \text{or} \quad h = -3
\]

Would you like further clarification, or do you have any additional questions? 

Here are 5 related questions to expand on this:
1. How do you solve quadratic equations that do not have perfect squares?
2. What happens if the discriminant is negative in a quadratic equation?
3. How would you solve an equation like \( h^2 - 13 = -5 \)?
4. Can you explain why there are two solutions for \( h \)?
5. How do square roots relate to graphing quadratic equations?

**Tip:** Always remember to check both the positive and negative square roots when solving equations like these.

Learn how to solve the quadratic equation h^2 - 13 = -4 by isolating the variable and taking the square root. This problem involves key algebraic concepts, perfect squares, and the square root principle. Ideal for students in Grades 7-9.

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