Question

Solve the square root equation 2x−−√=x+6−−−−√ .(1 point)
Responses

x=6
x equals 6

x=2
x equals 2

x=−6
x equals negative 6

x=65

Answer 1

To solve the equation \( \sqrt{2x} = \sqrt{x + 6} \), we can start by squaring both sides to eliminate the square roots:

\[
2x = x + 6
\]

Next, we will rearrange the equation:

\[
2x - x = 6
\]
\[
x = 6
\]

Now, we need to check whether \( x = 6 \) is a valid solution by substituting it back into the original equation:

\[
\sqrt{2(6)} = \sqrt{6 + 6}
\]
\[
\sqrt{12} = \sqrt{12}
\]

Since both sides are equal, \( x = 6 \) is indeed a valid solution. Hence, the answer is:

**x = 6**.