Use the square root property to solve the quadratic equation.

Question

2xsquaredminus6equals0
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Part 1
x​ =
  
enter your response here

Answer 1

To solve the quadratic equation \( 2x^2 - 6 = 0 \) using the square root property, we can follow these steps:

1. Isolate the quadratic term: \[ 2x^2 = 6 \]

2. Divide both sides by 2: \[ x^2 = 3 \]

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

Thus, the solutions to the equation are: \[ x = \sqrt{3} \quad \text{and} \quad x = -\sqrt{3} \]

So, to enter the response for \( x \):

• One solution is \( x = \sqrt{3} \)
• The other solution is \( x = -\sqrt{3} \)

You can represent it concisely by saying: \[ x = \pm \sqrt{3} \]