Explanation
We are given the following equation:
[tex]\sqrt{2x}=x-4[/tex]We are required to determine the value of x in the given equation.
This is achieved thus:
[tex]\begin{gathered} \sqrt{2x}=x-4 \\ \text{ Square both sides} \\ (\sqrt{2x})^2=(x-4)^2 \\ 2x=x^2-8x+16 \\ x^2-10x+16=0 \\ (x-2)(x-8)=0 \\ x-2=0;x-8=0 \\ x=2;x=8 \end{gathered}[/tex]Substituting the values of x in the original equation, we have:
[tex]\begin{gathered} \sqrt{2x}=x-4 \\ where\text{ }x=2 \\ \sqrt{2\cdot2}=2-4 \\ \sqrt{4}=-2 \\ 2=-2(False) \\ \\ \sqrt{2x}=x-4 \\ where\text{ }x=8 \\ \sqrt{2\cdot8}=8-4 \\ \sqrt{16}=4 \\ 4=4(True) \end{gathered}[/tex]Hence, the answer is:
[tex]x=8[/tex]