To solve the equation \( x^2 - 42 = 0 \), follow these steps:

1. Start by isolating \( x^2 \) on one side of the equation:
   \[
   x^2 = 42
   \]

2. Next, take the square root of both sides to solve for \( x \):
   \[
   x = \pm \sqrt{42}
   \]

3. Simplify the square root (if possible):
   \[
   x = \pm \sqrt{42}
   \]

Since 42 does not have a perfect square factor, the answer remains \( x = \pm \sqrt{42} \).

Thus, the solutions are:
\[
x = \sqrt{42} \quad \text{or} \quad x = -\sqrt{42}
\]

Would you like more details or have any questions about this solution?

Here are some related questions:

1. How do you solve equations involving higher powers of \( x \), like \( x^3 - 42 = 0 \)?
2. What is the approximate decimal value of \( \sqrt{42} \)?
3. How would the solution change if the equation were \( x^2 + 42 = 0 \)?
4. Can you solve \( x^2 - 42 = 0 \) by factoring?
5. How does the Discriminant help in solving quadratic equations?

**Tip:** When solving quadratic equations, always check if the square root can be simplified for an exact solution.

Learn how to solve the quadratic equation x^2 - 42 = 0 step-by-step. This problem involves algebraic manipulation and finding square roots. Suitable for students in Grades 7-9.

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