what method would you choose to solve the equation 2x² - 7 = 9? explain why you chose this method.

Explanation:

Step1: Isolate the $x^{2}$ - term

First, add 7 to both sides of the equation $2x^{2}-7 = 9$. We get $2x^{2}=9 + 7$, so $2x^{2}=16$. Then divide both sides by 2, resulting in $x^{2}=8$. $2x^{2}-7+7=9 + 7$; $\frac{2x^{2}}{2}=\frac{16}{2}$

Step2: Solve for $x$

Take the square - root of both sides. Since $x^{2}=8$, then $x=\pm\sqrt{8}=\pm2\sqrt{2}$. $x=\pm\sqrt{8}$

Answer:

The square - root method is chosen. First, we isolate the $x^{2}$ term by performing arithmetic operations to get $x^{2}=8$. Then, we take the square root of both sides to find the values of $x$. The solutions are $x = 2\sqrt{2}$ and $x=-2\sqrt{2}$.