Solve #5 – 6 by the Square Root Property
5. (x + 8)2 = 52 6. (2x – 3)2 + 4 = 29

Let's solve the equations using the Square Root Property.

### Problem 5: \((x + 8)^2 = 52\)

1. Start by taking the square root of both sides:
   \[
   \sqrt{(x + 8)^2} = \pm \sqrt{52}
   \]
   Simplifying, we get:
   \[
   x + 8 = \pm \sqrt{52}
   \]

2. Simplify \(\sqrt{52}\):
   \[
   \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13}
   \]
   So the equation becomes:
   \[
   x + 8 = \pm 2\sqrt{13}
   \]

3. Isolate \(x\) by subtracting 8 from both sides:
   \[
   x = -8 \pm 2\sqrt{13}
   \]

So the solutions are:
\[
x = -8 + 2\sqrt{13} \quad \text{or} \quad x = -8 - 2\sqrt{13}
\]

### Problem 6: \((2x - 3)^2 + 4 = 29\)

1. Start by isolating the squared term:
   \[
   (2x - 3)^2 = 29 - 4
   \]
   Simplifying, we get:
   \[
   (2x - 3)^2 = 25
   \]

2. Take the square root of both sides:
   \[
   \sqrt{(2x - 3)^2} = \pm \sqrt{25}
   \]
   Simplifying, we get:
   \[
   2x - 3 = \pm 5
   \]

3. Solve for \(x\) by considering the two possible cases:
   - Case 1: \(2x - 3 = 5\)
     \[
     2x = 8 \quad \Rightarrow \quad x = 4
     \]
   - Case 2: \(2x - 3 = -5\)
     \[
     2x = -2 \quad \Rightarrow \quad x = -1
     \]

So the solutions are:
\[
x = 4 \quad \text{or} \quad x = -1
\]

Would you like more details on any of these steps, or do you have any questions?

### Related Questions:
1. What is the Square Root Property and how does it work?
2. Can you solve \( (x - 7)^2 = 81 \) using the Square Root Property?
3. How can you simplify square roots like \( \sqrt{52} \) step-by-step?
4. What are some common mistakes to avoid when using the Square Root Property?
5. Can you apply the Square Root Property to solve \( (3x + 2)^2 = 36 \)?

**Tip:** When using the Square Root Property, always remember to consider both the positive and negative roots.

Learn how to solve quadratic equations (x + 8)^2 = 52 and (2x - 3)^2 + 4 = 29 using the Square Root Property with step-by-step solutions. This problem involves applying the Square Root Property to isolate variables and solve for x. Suitable for high school students.

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