To solve the quadratic equation \( 6x^2 - 225 = 0 \), follow these steps:

1. **Isolate the quadratic term**:
   \[
   6x^2 = 225
   \]

2. **Divide both sides by 6** to simplify:
   \[
   x^2 = \frac{225}{6} = 37.5
   \]

3. **Take the square root of both sides**:
   \[
   x = \pm \sqrt{37.5}
   \]

4. **Simplify the square root** (if possible):
   \[
   x = \pm \sqrt{37.5} = \pm \sqrt{\frac{75}{2}} = \pm \frac{\sqrt{75}}{\sqrt{2}}
   \]

   Simplify further:
   \[
   x = \pm \frac{5\sqrt{3}}{\sqrt{2}} \approx \pm 6.12
   \]

So, the solutions are approximately:
\[
x \approx \pm 6.12
\]

Would you like more details on any part of this solution, or do you have any other questions?

Here are 8 related questions you might find interesting:

1. What is the general process for solving quadratic equations?
2. How do you simplify square roots, and when is it necessary?
3. What are the possible types of solutions for quadratic equations?
4. How do you complete the square for a quadratic equation?
5. How is the quadratic formula derived and when is it used?
6. How can you solve quadratic equations by factoring?
7. What is the discriminant, and what does it tell us about the solutions of a quadratic equation?
8. How do quadratic equations relate to parabolas in graphing?

**Tip:** Always check if the quadratic equation can be factored easily before using the quadratic formula or other methods. This can save time!

Learn how to solve the quadratic equation 6x^2 - 225 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic equation formula and the quadratic formula theorem. Suitable for students in Grades 7-9.

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