Question

In the following exercises, solve each equation.

$y^2+64=0$

Short answer

The solution of the equation is$y=64i,-64i$

Step-by-step solution

Step 1. Given information

In the given question we have to solve given equation.

$y^2+64=0$

Step 2. The given equation is y2+64=0

Isolate the quadratic term.

Subtract 64 on both side

$$\begin{gathered} y^2+64-64=0-64 \\ {y}^2=-64 \end{gathered}$$

Step 3. Use the Square Root Property.

$y=\pm \sqrt{-64}$

Simplify using complex numbers.

We know $i^2=-1$

localid="1645597211373" $y=\pm \sqrt{64i^2}$

Step 4. Simplify the radical.

$y=\pm 64i$

Rewrite to show two solutions.

$y=64iy=-64i$