To solve the quadratic equation \(3x^2 - 23 = -35\), follow these steps:

1. **Move all terms to one side of the equation:**

   \[
   3x^2 - 23 + 35 = 0
   \]

   Simplify the equation:

   \[
   3x^2 + 12 = 0
   \]

2. **Isolate the quadratic term:**

   Subtract 12 from both sides:

   \[
   3x^2 = -12
   \]

3. **Solve for \(x^2\):**

   Divide both sides by 3:

   \[
   x^2 = -4
   \]

4. **Solve for \(x\):**

   Take the square root of both sides:

   \[
   x = \pm \sqrt{-4}
   \]

   Since the square root of a negative number involves an imaginary unit \(i\), we have:

   \[
   x = \pm 2i
   \]

Thus, the solutions are \(x = 2i\) and \(x = -2i\).

Would you like more details on any of the steps or have any questions?

Here are 5 related questions:
1. How do you solve quadratic equations with real solutions?
2. What are imaginary numbers, and how do they differ from real numbers?
3. Can you explain the process of completing the square to solve a quadratic equation?
4. How do you factor a quadratic equation with complex roots?
5. What is the quadratic formula, and when is it used?

**Tip:** When dealing with negative square roots, always remember they lead to imaginary numbers!

Learn how to solve the quadratic equation 3x² - 23 = -35 with a detailed step-by-step solution. This problem involves algebraic manipulation and complex number solutions. Suitable for advanced high school students and above.

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