Question

In the following exercises, solve each equation.

$x^2+25=0$

Short answer

The solution of the equation is$x=+5i,-5i$

Step-by-step solution

Step 1. Given information

In the given question we have to solve given equation.

$x^2+25=0$

Step 2. The given equation is x2+25=0

Isolate the quadratic term.

Subtract 25 on both side

$$\begin{gathered} x^2+25-25=0-25 \\ {x}^2=-25 \end{gathered}$$

Step 3. Use the Square Root Property.

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

Simplify using complex numbers.

We know $i^2=-1$

$x=\pm \sqrt{25i^2}$

Simplify the radical.

$x=\pm 5i$

Step 4. Rewrite to show two solutions.

$x=\pm 5i$

$x=5ix=-5i$