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Let's solve each of these quadratic equations using the **extracting square roots** method, where applicable.

### 1. \( x^2 = 169 \)

To solve:
\[
x = \pm \sqrt{169}
\]
\[
x = \pm 13
\]

**Solution:** \( x = 13 \) or \( x = -13 \)

---

### 2. \( x^2 + 3 = 39 \)

First, isolate \( x^2 \):
\[
x^2 = 39 - 3
\]
\[
x^2 = 36
\]

Now, take the square root:
\[
x = \pm \sqrt{36}
\]
\[
x = \pm 6
\]

**Solution:** \( x = 6 \) or \( x = -6 \)

---

### 3. \( 5x^2 - 7 = 118 \)

Isolate \( x^2 \):
\[
5x^2 = 118 + 7
\]
\[
5x^2 = 125
\]
\[
x^2 = \frac{125}{5}
\]
\[
x^2 = 25
\]

Take the square root:
\[
x = \pm \sqrt{25}
\]
\[
x = \pm 5
\]

**Solution:** \( x = 5 \) or \( x = -5 \)

---

### 4. \( x^2 + 103 = 3 \)

Isolate \( x^2 \):
\[
x^2 = 3 - 103
\]
\[
x^2 = -100
\]

Since \( x^2 = -100 \) has no real solutions (square roots of negative numbers are not real), this equation has **no real solutions**.

**Solution:** No real solutions.

---

### 5. \( 4x^2 - 32 = 0 \)

Isolate \( x^2 \):
\[
4x^2 = 32
\]
\[
x^2 = \frac{32}{4}
\]
\[
x^2 = 8
\]

Now, take the square root:
\[
x = \pm \sqrt{8}
\]
\[
x = \pm 2\sqrt{2}
\]

**Solution:** \( x = 2\sqrt{2} \) or \( x = -2\sqrt{2} \)

---

Let me know if you have any questions about these solutions or need further clarification!

Here are some related questions:
1. How would you solve these equations using factoring instead of square roots?
2. What are some real-world applications of quadratic equations?
3. How would these solutions change if we were looking for complex roots?
4. Why does \( x^2 = -100 \) have no real solution?
5. Can these methods be extended to equations of higher degree, like \( x^4 \)?

**Tip:** Always check if the equation can be simplified before taking square roots. This can make the solving process faster and more accurate!

Solve the following quadratic equations using the extracting square root method: 1. x^2 = 169, 2. x^2 + 3 = 39, 3. 5x^2 - 7 = 118, 4. x^2 + 103 = 3, 5. 4x^2 - 32 = 0

Learn how to solve quadratic equations like x^2 = 169, 5x^2 - 7 = 118, and more using the extracting square roots method. Includes step-by-step solutions for each problem. Suitable for students in Grades 8-10.

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