https://file.aiquickdraw.com/mathbot/file/1728567070376h36h4wla.jpg

The problem shown in the image is asking to solve for \( p \) using the square root property. The given equation is:

\[
8(p + 7)^2 + 28 = 60
\]

### Step-by-step solution:

1. **Subtract 28 from both sides** to isolate the squared term:
   \[
   8(p + 7)^2 = 60 - 28
   \]
   \[
   8(p + 7)^2 = 32
   \]

2. **Divide both sides by 8**:
   \[
   (p + 7)^2 = \frac{32}{8}
   \]
   \[
   (p + 7)^2 = 4
   \]

3. **Take the square root of both sides**:
   \[
   p + 7 = \pm \sqrt{4}
   \]
   \[
   p + 7 = \pm 2
   \]

4. **Solve for \( p \)** by subtracting 7 from both sides:
   - For the positive root:
     \[
     p = 2 - 7 = -5
     \]
   - For the negative root:
     \[
     p = -2 - 7 = -9
     \]

### Final answer:
The solutions for \( p \) are \( p = -5 \) and \( p = -9 \).

Would you like any more details or have any questions? Here are some related questions to expand your understanding:

1. What is the significance of the square root property in solving quadratic equations?
2. Can the square root method be used for all quadratic equations?
3. How do you handle equations where the term inside the square root is negative?
4. What are other methods to solve quadratic equations apart from the square root property?
5. How would the solution change if the constant on the right side of the equation were different?

**Tip:** Always remember to consider both the positive and negative square roots when solving equations involving squares!

Solve for p using the square root property: 8(p + 7)^2 + 28 = 60

Learn how to solve the quadratic equation 8(p + 7)^2 + 28 = 60 using the square root property. This solution demonstrates how to isolate the squared term, take the square root of both sides, and solve for the variable p. Suitable for high school students in Grades 9-11.

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