https://file.aiquickdraw.com/mathbot/file/1727723120226jmqqi2ou.jpg

It seems like the image contains the equation:

\[
7x^2 + 21 = 0
\]

To solve this equation, follow these steps:

1. Start with the equation:
   \[
   7x^2 + 21 = 0
   \]

2. Subtract 21 from both sides:
   \[
   7x^2 = -21
   \]

3. Divide both sides by 7:
   \[
   x^2 = -3
   \]

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

   Since \(\sqrt{-3}\) involves an imaginary number, we can express the solutions as:
   \[
   x = \pm i\sqrt{3}
   \]

Therefore, the two solutions are \(x = i\sqrt{3}\) and \(x = -i\sqrt{3}\).

Would you like further details or clarifications on these steps?

Here are 5 related questions:
1. How do you solve quadratic equations with real-number solutions?
2. What are imaginary numbers and how do they arise in equations?
3. Can you explain how to handle equations with complex numbers?
4. What does it mean when a quadratic equation has no real solution?
5. How do we graph solutions involving imaginary numbers?

**Tip:** Quadratic equations can have real or complex (imaginary) solutions depending on the discriminant \(\Delta = b^2 - 4ac\). If \(\Delta < 0\), the solutions involve imaginary numbers.

Learn how to solve the quadratic equation 7x^2 + 21 = 0. This step-by-step guide explains key algebraic concepts, including imaginary numbers, and the process to find the solutions x = i√3 and x = -i√3. Suitable for students in Grades 9-12.

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