x2+25=0

To solve the equation \( x^2 + 25 = 0 \), we can isolate \( x^2 \) by moving 25 to the other side:

\[ x^2 = -25 \]

Next, we take the square root of both sides. Since we are dealing with a negative number, we will introduce the imaginary unit \( i \) (where \( i = \sqrt{-1} \)):

\[ x = \pm \sqrt{-25} \]

This simplifies to:

\[ x = \pm 5i \]

Thus, the solutions to the equation \( x^2 + 25 = 0 \) are:

\[ x = 5i \quad \text{and} \quad x = -5i \]