Question

Solve the quadratic equation by the square root property.
2 x squared equals 8

Answer 1

To solve the quadratic equation \( 2x^2 = 8 \) using the square root property, follow these steps:

1. First, divide both sides of the equation by 2 to simplify it:

\[
x^2 = \frac{8}{2}
\]

\[
x^2 = 4
\]

2. Next, apply the square root property. The square root property states that if \( x^2 = a \), then \( x = \sqrt{a} \) or \( x = -\sqrt{a} \). Here, we take the square root of both sides:

\[
x = \sqrt{4} \quad \text{or} \quad x = -\sqrt{4}
\]

\[
x = 2 \quad \text{or} \quad x = -2
\]

3. Therefore, the solutions to the equation \( 2x^2 = 8 \) are:

\[
x = 2 \quad \text{and} \quad x = -2
\]

So, the final answer is \( x = 2 \) and \( x = -2 \).