Questions: Solve x^2 = 63, where x is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. If there is no solution, click "No solution."

Solve x^2 = 63, where x is a real number.
Simplify your answer as much as possible.

If there is more than one solution, separate them with commas.
If there is no solution, click "No solution."

Transcript text: Solve $x^{2}=63$, where $x$ is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. If there is no solution, click "No solution."

Solution

Solution Steps

Step 1: Take the square root of both sides

Taking the square root of both sides of the equation $x^2 = 63$ gives us $\sqrt{x^2} = \sqrt{63}$.

Step 2: Simplify the square roots

$\sqrt{x^2}$ simplifies to $|x|$, which means $x$ can be positive or negative. $\sqrt{63}$ can be simplified as $\sqrt{9 \cdot 7} = \sqrt{9} \cdot \sqrt{7} = 3\sqrt{7}$. So, $|x| = 3\sqrt{7}$.

Step 3: Account for positive and negative solutions

Since $|x| = 3\sqrt{7}$, the solutions are $x = 3\sqrt{7}$ and $x = -3\sqrt{7}$.