Question

In the following exercises, solve each equation.

$y^2+45=0$

Short answer

The solution of the equation is$y=3i\sqrt{5},-3i\sqrt{5}$

Step-by-step solution

Step 1. Given information

In the given question we have to solve given equation.

$y^2+45=0$

Step 2. The given equation is y2+45=0

Isolate the quadratic term.

Subtract 45 on both side

$$\begin{gathered} y^2+45-45=0-45 \\ {y}^2=-45 \end{gathered}$$

Step 3. Use the Square Root Property.

$y=\pm \sqrt{-45}$

Simplify using complex numbers.

We know $i^2=-1$

$y=\pm \sqrt{45i^2}$

Step 4. Simplify the radical.

$$\begin{gathered} y=\pm \sqrt{5\times 9i^2} \\ y=\pm 3i\sqrt{5} \end{gathered}$$

Rewrite to show two solutions.

$y=3i\sqrt{5}y=-3i\sqrt{5}$