The equation is:

$x^2 + 25 = 0$

To solve for $x$, we can isolate $x^2$ by moving $25$ to the other side of the equation:

$x^2 = -25$

To solve for $x$, we take the square root of both sides. However, the square root of a negative number requires complex numbers:

$x = \pm \sqrt{-25}$

Using the imaginary unit $i$ where $i = \sqrt{-1}$, we get:

$x = \pm 5i$

Solution

$x = 5i \quad \text{or} \quad x = -5i$

Would you like a further explanation or have any questions?

Here are 5 related questions for further practice:

1. Solve $x^2 + 36 = 0$.
2. Solve $x^2 - 16 = 0$.
3. Find the roots of $x^2 + 9 = 0$.
4. Solve $x^2 + 1 = 0$.
5. Solve $x^2 - 25 = 0$.

Tip: When taking the square root of a negative number, use the imaginary unit $i$.