Question

Find the real solutions of the equation$2x^2=8$ by factoring.

Short answer

The real solution of the equation is $x=-2\text{and}x=2$.

Step-by-step solution

Step 1. Factorized the given quadratic equation.

$$\begin{gathered} 2x^2=8....\left(\text{Given}\right) \\ {x}^2=4....\left(\text{Divideby}2\right) \\ {x}^2-4=0 \\ \left(x+2\right)\left(x-2\right)=0....\left(\text{Factorized}\right) \\ \left(x+2\right)\left(x-2\right)=0....\left(1\right) \end{gathered}$$

Step 2. Further simplifying (1).

$$\begin{gathered} \left(x+2\right)\left(x-2\right)=0....\left(\text{From}\left(1\right)\right) \\ x-2=0\text{or}x+2=0 \\ x=2\text{or}x=-2 \end{gathered}$$

Step 3. Description of steps.

From the obtained values, the real solution of the equation is $x=-2\text{and}x=2$.