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The equation provided is:

\[
338 - 6x^2 = 0
\]

To solve for \( x \), we can rearrange the equation and isolate \( x \) as follows:

### Step 1: Move \( 6x^2 \) to the other side
\[
338 = 6x^2
\]

### Step 2: Divide both sides by 6
\[
x^2 = \frac{338}{6}
\]
\[
x^2 = 56.3333\ldots
\]

### Step 3: Take the square root of both sides
\[
x = \pm \sqrt{56.3333}
\]
\[
x \approx \pm 7.5067
\]

### Solution
The approximate solutions are:
\[
x \approx 7.51 \quad \text{and} \quad x \approx -7.51
\]

Would you like a detailed explanation of each step or have any additional questions?

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Here are 5 related questions for further practice:

1. How would you solve \( 338 - 7x^2 = 0 \)?
2. What are the solutions to the equation \( 400 - 8x^2 = 0 \)?
3. How do you solve an equation in the form \( a - bx^2 = 0 \)?
4. What are the steps for solving \( 338 - 6x^2 = 5 \)?
5. How would the solutions change if we used \( 338 + 6x^2 = 0 \)?

**Tip:** When dealing with equations of the form \( a - bx^2 = 0 \), isolating \( x^2 \) makes it easy to find \( x \) by taking the square root.

Learn how to solve the quadratic equation 338 - 6x^2 = 0 with a detailed step-by-step approach. This problem covers essential algebraic concepts and is suitable for students in Grades 7-9.

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