Solve the Quadratic Equation 2x² - 8 = 0: Finding the Roots

To solve the quadratic equation $2x^2 - 8 = 0$, we will follow these steps:

• Step 1: Isolate $x^2$.
• Step 2: Solve for $x$ by taking square roots.

Let's perform each step:

Step 1: Isolate $x^2$
Start with the given equation:
$2x^2 - 8 = 0$

Add 8 to both sides to isolate the term involving $x$:
$2x^2 = 8$

Divide both sides by 2 to solve for $x^2$:
$x^2 = 4$

Step 2: Solve for $x$ by taking square roots
Take the square root of both sides, remembering to consider both the positive and negative roots:
$x = \pm \sqrt{4}$

Simplify the square root:
$x = \pm 2$

This means there are two solutions:
$x_1 = 2$ and $x_2 = -2$

Therefore, the solutions to the equation $2x^2 - 8 = 0$ are $x_1 = -2, x_2 = 2$.

Matching this with the choices provided, the correct answer is choice 3: $x_1 = -2, x_2 = 2$.