Solve using the square root property.

Question

x squared minus 63x2−63equals=00
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Part 1
xequals= enter your response here
​(Simplify your answer. Type an exact​ answer, using radicals as needed. Use a comma to separate answers as​ needed.)

Answer 1

To solve the equation \( x^2 - 63 = 0 \) using the square root property, you can follow these steps:

1. Isolate the \( x^2 \) term: \[ x^2 = 63 \]

2. Take the square root of both sides: Remember that when you take the square root of both sides, you need to consider both the positive and negative roots. \[ x = \pm \sqrt{63} \]

3. Simplify \( \sqrt{63} \): The number 63 can be factored as \( 9 \times 7 = 3^2 \times 7 \). Therefore, \[ \sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7} \]

4. Write the solution: So, the solutions for \( x \) are: \[ x = 3\sqrt{7}, -3\sqrt{7} \]

Thus, the final answer is: \[ x = 3\sqrt{7}, -3\sqrt{7} \]