Q. 432 - Intermediate Algebra

Question

In the following exercises, solve.

$4n^2=36$

Step-by-Step Solution

Answer

Answer is $n=3,n=-3$

Step 1. Given

The equation is $4n^2=36$

Step 2. Simplify the equation

$$\begin{gathered} 4n^2=36 \\ 4n^2-36=0 \\ {n}^2-9=0 \\ (n+3)(n-3)=0 \end{gathered}$$

So,

$$\begin{gathered} n+3=0 \\ n=-3 \end{gathered}$$

and

$$\begin{gathered} n-3=0 \\ n=3 \end{gathered}$$

Step 3. Check both the values

Put $n=3$ in original equation,

$$\begin{gathered} 4n^2=36 \\ 4{\left(3\right)}^2=36 \\ 36=36 \end{gathered}$$

True

Now put $n=-3$ in original equation,

$$\begin{gathered} 4n^2=36 \\ 4{(-3)}^2=36 \\ 36=36 \end{gathered}$$

True

Step 4. Required answer

Answer is $n=3,n=-3$