https://file.aiquickdraw.com/mathbot/file/1728952636029d2aul7li.jpg

The quadratic equation in the image is:

\[
x^2 + 40 = 0
\]

### Solving for \(x\):

1. Start by isolating \(x^2\):
   \[
   x^2 = -40
   \]

2. Take the square root of both sides:
   \[
   x = \pm \sqrt{-40}
   \]

3. Simplify the square root:
   \[
   x = \pm \sqrt{-1 \times 40}
   \]
   Using \( \sqrt{-1} = i \) (the imaginary unit), we get:
   \[
   x = \pm i\sqrt{40}
   \]

4. Simplify \( \sqrt{40} \):
   \[
   \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10}
   \]
   So, the solution is:
   \[
   x = \pm 2i\sqrt{10}
   \]

Thus, the solutions to the equation \(x^2 + 40 = 0\) are:
\[
x = 2i\sqrt{10} \quad \text{or} \quad x = -2i\sqrt{10}
\]

Would you like further clarification or additional details?

### Related Questions:
1. How do you solve a quadratic equation that has real solutions?
2. What are imaginary numbers, and how are they used in solving equations?
3. Can every quadratic equation have imaginary solutions?
4. How do you simplify square roots involving negative numbers?
5. How would the solution change if the constant term were positive instead of negative?

### Tip:
Always check for imaginary solutions when dealing with negative values under square roots!

Solve the following quadratic equation: x^2 + 40 = 0

Learn how to solve the quadratic equation x^2 + 40 = 0 with detailed step-by-step instructions. This problem introduces imaginary numbers and involves simplifying square roots with negative values. Ideal for students in Grades 9-10.

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