Question

Find the real solutions of the equation$3x^2-27=0$ by factoring.

Short answer

The real solution of the equation is $x=-3\text{and}x=3$.

Step-by-step solution

Step 1. Factorized the given quadratic equation.

$$\begin{gathered} 3x^2-27=0....\left(\text{Given}\right) \\ {x}^2-9=0....\left(\text{Divideby}3\right) \\ {\left(x\right)}^2-{\left(3\right)}^2=0 \\ \left(x+3\right)\left(x-3\right)=0....\left(\text{Factorized}\right) \\ \left(x+3\right)\left(x-3\right)=0....\left(1\right) \end{gathered}$$

Step 2. Further simplifying (1).

$$\begin{gathered} \left(x+3\right)\left(x-3\right)=0....\left(\text{From}\left(1\right)\right) \\ x-3=0\text{or}x+3=0 \\ x=3\text{or}x=-3 \end{gathered}$$

Step 3. DESCRIPTION OF STEPS.

From the obtained values, the real solution of the equation is $x=-3\text{and}x=3$.