Question

How do you factor and solve $x^2=81$?

Answer 1

To solve the given equation:

Consider the given equation.

$x^2=81$

Rewrite the above equation:

$$\begin{gathered} x^2-81=0 \\ \Rightarrow x^2-9^2=0 \end{gathered}$$

Using the property $a^2-b^2=\left(a+b\right)\left(a-b\right)$ and find the solutions in below:

$\begin{array}{rcl}\left(x+9\right)\left(x-9\right)& =& 0\left[\text{Use the property}:\left(a^2-b^2=\left(a+b\right)\left(a-b\right)\right)\right]\\ & \Rightarrow & x+9=0orx-9=0\left[\text{Simplifying}\right]\\ \therefore x& =& -9orx=9\end{array}$

Hence, the solutions of the given equation is $\mathbf{-}\mathbf{9}\text{and}\mathbf{9}$.