The given equation is \( |x^2 - 3| = 2 \).

To solve it, we need to consider the definition of absolute value. The equation \( |A| = B \) implies that \( A = B \) or \( A = -B \).

### Step 1: Set up two separate equations
1. \( x^2 - 3 = 2 \)
2. \( x^2 - 3 = -2 \)

### Step 2: Solve each equation
**For the first equation:**
\[
x^2 - 3 = 2
\]
Add 3 to both sides:
\[
x^2 = 5
\]
Take the square root of both sides:
\[
x = \pm \sqrt{5}
\]

**For the second equation:**
\[
x^2 - 3 = -2
\]
Add 3 to both sides:
\[
x^2 = 1
\]
Take the square root of both sides:
\[
x = \pm 1
\]

### Step 3: Combine the solutions
The solutions are:
\[
x = \pm \sqrt{5}, \pm 1
\]

So, the complete solution is:
\[
x = \sqrt{5}, \, x = -\sqrt{5}, \, x = 1, \, x = -1
\]

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. Solve \( |x^2 - 4| = 3 \).
2. Solve \( |x^2 - 2x + 1| = 0 \).
3. Solve \( |2x - 5| = 7 \).
4. What is the solution to \( |3x + 1| = 4x + 5 \)?
5. Solve \( |x^2 + 2x - 8| = 0 \).

**Tip:** When solving absolute value equations, always remember to consider both the positive and negative scenarios.

This tutorial provides a detailed solution to the absolute value equation |x^2 - 3| = 2. Learn how to break down the problem, solve quadratic equations, and apply the square root property. Ideal for students in Grades 9-10.

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