Quadratic Conundrum: Solving 2x² - 8 = x^2 + 4

Let's solve the equation step-by-step:

• Step 1: Rearrange the equation.

We start with the given equation:

$2x^2 - 8 = x^2 + 4$

Subtract $x^2 + 4$ from both sides to get:

$2x^2 - 8 - x^2 - 4 = 0$

• Step 2: Simplify the equation.

Combine the like terms:

$(2x^2 - x^2) - 8 - 4 = 0$

This simplifies to:

$x^2 - 12 = 0$

• Step 3: Solve for $x$.

Add 12 to both sides:

$x^2 = 12$

Now take the square root of both sides:

$x = \pm \sqrt{12}$

Given the choices, the correct answer is $\pm \sqrt{12}$.