Question

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

Explanation:

Step1: Isolate the quadratic term

Add 7 to both sides to isolate $2x^2$.
$2x^2 - 7 + 7 = 9 + 7$
$2x^2 = 16$

Step2: Solve for $x^2$

Divide both sides by 2 to get $x^2$ alone.
$\frac{2x^2}{2} = \frac{16}{2}$
$x^2 = 8$

Step3: Solve for x using square roots

Take the square root of both sides, accounting for positive and negative roots.
$x = \pm\sqrt{8} = \pm2\sqrt{2}$

Answer:

I would use the isolating the variable + square root method. This equation is a simple quadratic with no linear ($x$) term, so isolating $x^2$ and taking square roots is the most straightforward, efficient approach—no need for factoring, completing the square, or the quadratic formula. The final solutions are $x=2\sqrt{2}$ and $x=-2\sqrt{2}$.