Use the square root property to solve the quadratic equation.

Question

5xsquaredminus10equals0
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Part 1
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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: \[ x = \sqrt{2}, , -\sqrt{2} \]