Question

Use the square root property to solve the quadratic equation.
5xsquaredminus10equals0
.
.
.
Question content area right
Part 1
x​ =
  
enter your response here

Answer 1

To solve the quadratic equation \( 5x^2 - 10 = 0 \) using the square root property, follow these steps:

1. **Isolate the \( x^2 \) term:**
\[
5x^2 - 10 = 0
\]
Add \( 10 \) to both sides:
\[
5x^2 = 10
\]

2. **Divide by 5:**
\[
x^2 = \frac{10}{5}
\]
Simplifying gives:
\[
x^2 = 2
\]

3. **Apply the square root property:**
The square root property states that if \( x^2 = k \), then \( x = \pm \sqrt{k} \).
\[
x = \pm \sqrt{2}
\]

So, the solutions to the equation are:
\[
x = \sqrt{2} \quad \text{and} \quad x = -\sqrt{2}
\]

Thus, the answer is:
\[
x = \sqrt{2}, \, -\sqrt{2}
\]