https://file.aiquickdraw.com/mathbot/file/1727030934586ialjfb9x.jpg

The equation provided in the image is \( 3x^2 + 108 = 0 \). To solve for \( x \), let's go through the steps.

### Step-by-Step Solution:

1. Start with the equation:
   \[
   3x^2 + 108 = 0
   \]

2. Subtract 108 from both sides:
   \[
   3x^2 = -108
   \]

3. Divide both sides by 3 to isolate \( x^2 \):
   \[
   x^2 = \frac{-108}{3} = -36
   \]

4. Take the square root of both sides:
   \[
   x = \pm \sqrt{-36}
   \]

5. Using the property of square roots with negative numbers, \( \sqrt{-36} = 6i \), where \( i \) is the imaginary unit:
   \[
   x = \pm 6i
   \]

### Conclusion:
The values of \( x \) that satisfy the equation are \( 6i \) and \( -6i \). From the choices provided, the correct answer is **6i**.

Would you like further details or explanations?

### 5 Related Questions:
1. What is the significance of the imaginary unit \( i \) in complex numbers?
2. How do we handle square roots of negative numbers?
3. What is the general method for solving quadratic equations like this one?
4. Can quadratic equations have both real and imaginary solutions?
5. How can we represent complex solutions graphically on the complex plane?

### Tip:
When solving quadratic equations with negative numbers under the square root, always remember to factor in the imaginary unit \( i \).

What value of x will satisfy the equation 3x² + 108 = 0?

Find the value of x that satisfies the equation 3x² + 108 = 0. This algebra problem explores solving quadratic equations with complex numbers, involving the imaginary unit i. Suitable for students in Grades 9-12.

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