Question

Solve$q^2+24=0$

Short answer

The solutions of the quadratic equation:$q=2\sqrt{6}i,q=-2\sqrt{6}i$

Step-by-step solution

Step 1. Given information

Consider the quadratic equation

$q^2+24=0$

The objective is to solve the quadratic equation by using square root property.

If$x^2=k$, then$x=\pm \sqrt{k}$

Isolate the quadratic term.

$q^2=-24$

Use the Square Root Property.

localid="1645358604148" $q=\pm \sqrt{-24}$

Step 2. Simplify the expression. 

Simplify using complex numbers.

$q=\pm \sqrt{24}i$

Simplify the radical.

$q=\pm 2\sqrt{6}i$

Rewrite to show two solutions.

$q=2\sqrt{6}i,q=-2\sqrt{6}i$

Step 3. Check the solutions: 

Substitute $q=2\sqrt{6}i$in the original equation.

$$\begin{gathered} q^2+24=0 \\ {\left(2\sqrt{6}i\right)}^2+24\stackrel{?}{=}0 \\ 4\left(6\right)i^2+24\stackrel{?}{=}0 \\ 24(-1)+24\stackrel{?}{=}0 \\ 0=0 \end{gathered}$$

Substitute $q=-2\sqrt{6}i$in the original equation.

$$\begin{gathered} q^2+24=0 \\ {(-2\sqrt{6}i)}^2+24\stackrel{?}{=}0 \\ 4\left(6\right)i^2+24\stackrel{?}{=}0 \\ 24(-1)+24\stackrel{?}{=}0 \\ 0=0 \end{gathered}$$