https://file.aiquickdraw.com/mathbot/file/1726366001623lr06v2wk.jpg

The two equations from the image are:

1. \( x^2 - 4 = 0 \) (equation 46)
2. \( x^2 + 2x + 1 = 0 \) (equation 47)

Let's solve each one:

### 1. Solving \( x^2 - 4 = 0 \)

This is a simple quadratic equation that can be solved by factoring or taking square roots.

\[
x^2 - 4 = (x - 2)(x + 2) = 0
\]

Thus, the solutions are:

\[
x - 2 = 0 \quad \text{or} \quad x + 2 = 0
\]
\[
x = 2 \quad \text{or} \quad x = -2
\]

### 2. Solving \( x^2 + 2x + 1 = 0 \)

This is also a quadratic equation. We can factor it as follows:

\[
x^2 + 2x + 1 = (x + 1)^2 = 0
\]

Thus, the solution is:

\[
x + 1 = 0
\]
\[
x = -1
\]

### Summary of solutions:
- For \( x^2 - 4 = 0 \), the solutions are \( x = 2 \) and \( x = -2 \).
- For \( x^2 + 2x + 1 = 0 \), the solution is \( x = -1 \).

Would you like further details or clarification on any of these steps?

### Related Questions:
1. How do you solve more complex quadratic equations?
2. What is the discriminant, and how is it used in solving quadratic equations?
3. How can you solve quadratic equations using the quadratic formula?
4. Can quadratic equations have complex solutions?
5. What does the graph of a quadratic equation represent?

### Tip:
Always check if a quadratic equation can be factored easily before using the quadratic formula—it can save time!

Solve the quadratic equations: x^2 - 4 = 0 and x^2 + 2x + 1 = 0.

Learn how to solve the quadratic equations x^2 - 4 and x^2 + 2x + 1 with step-by-step solutions. This problem demonstrates the factoring method and zero product property. Suitable for students in Grades 7-9.

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