Let's solve the quadratic equation \(6x^2 - 225 = 0\).

### Step 1: Move the constant term to the right side
\[
6x^2 = 225
\]

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

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

### Step 4: Simplify the square root
\[
\sqrt{37.5} = \sqrt{\frac{75}{2}} = \frac{\sqrt{75}}{\sqrt{2}} = \frac{5\sqrt{3}}{\sqrt{2}} \approx 6.12
\]

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

Would you like a more detailed explanation, or do you have any other questions?

Here are 8 related questions that might interest you:

1. How do you find the exact value of square roots?
2. Can you solve \(6x^2 - 225 = 0\) by factoring?
3. What are the properties of quadratic equations?
4. How do you use the quadratic formula to solve equations?
5. What is the geometric interpretation of solving \(6x^2 - 225 = 0\)?
6. How do you solve quadratic equations with imaginary solutions?
7. What role does the discriminant play in solving quadratic equations?
8. Can you solve quadratic equations by completing the square?

**Tip:** Whenever you encounter a quadratic equation, check if it's possible to simplify it by dividing all terms by the greatest common factor before solving. This makes the calculation easier!

Learn how to solve the quadratic equation 6x^2 - 225 = 0 with a detailed step-by-step solution. This problem involves algebraic manipulation and square roots, applying the quadratic formula to find approximate solutions. Suitable for students in Grades 10-12.

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