Question

In the following exercises, solve each equation.

$x^2+63=0$

Short answer

The solution of the equation is$x=3i\sqrt{7},-3i\sqrt{7}$

Step-by-step solution

Step 1. Given information

In the given question we have to solve given equation.

$x^2+63=0$

Step 2. The given equation is x2+63=0

Isolate the quadratic term.

Subtract 63 on both side

$$\begin{gathered} x^2+63-63=0-63 \\ {x}^2=-63 \end{gathered}$$

Step 3. Use the Square Root Property.

$x=\pm \sqrt{-63}$

Simplify using complex numbers.

We know $i^2=-1$

$x=\pm \sqrt{63i^2}$

Step 4. Simplify the radical.

$$\begin{gathered} x=\pm \sqrt{7\times 9i^2} \\ x=\pm 3i\sqrt{7} \end{gathered}$$

Rewrite to show two solutions.

$x=3i\sqrt{7}x=-3i\sqrt{7}$