Question

Solve using the square root property.
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:
\[
x = 3\sqrt{7}, -3\sqrt{7}
\]