Question

Solve$c^2+12=0$

Short answer

The solutions of the quadratic equation:$c=2\sqrt{3}i,c=-2\sqrt{3}i$

Step-by-step solution

Step. Given information

Consider the quadratic equation

$c^2+12=0$

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.

$c^2=-12$

Use the Square Root Property.

$c=\pm \sqrt{-12}$

Step 2. Simplify the expression.

Simplify using complex numbers.

$c=\pm \sqrt{12}i$

Simplify the radical.

$c=\pm 2\sqrt{3}i$

Rewrite to show two solutions.

$c=2\sqrt{3}i,c=-2\sqrt{3}i$

Step 3. Check the solutions:

Substitute $c=2\sqrt{3}i$in the original equation.

$$\begin{gathered} c^2+12=0 \\ {\left(2\sqrt{3}i\right)}^2+12\stackrel{?}{=}0 \\ 4\left(3\right)i^2+12\stackrel{?}{=}0 \\ 12(-1)+12\stackrel{?}{=}0 \\ 0=0 \end{gathered}$$

Substitute $c=-2\sqrt{3}i$in the original equation.

$$\begin{gathered} c^2+12=0 \\ {(-2\sqrt{3}i)}^2+12\stackrel{?}{=}0 \\ 4\left(3\right)i^2+12\stackrel{?}{=}0 \\ 12(-1)+12\stackrel{?}{=}0 \\ 0=0 \end{gathered}$$