Answer:
[tex]x=13[/tex]
Step-by-step explanation:
Solving for x,
[tex]\begin{gathered} \sqrt{x-4}=x-10 \\ \rightarrow(\sqrt{x-4})^2=(x-10)^2 \\ \rightarrow x-4=x^2-20x+100 \\ \rightarrow x^2-21x+104=0 \\ \rightarrow(x-8)(x-13)=0 \\ \\ \rightarrow x_1=8 \\ \rightarrow x_2=13 \end{gathered}[/tex]
Now, we check the solutions to see which one is correct and which one isn't:
[tex]\begin{gathered} \sqrt{x-4}=x-10 \\ \rightarrow\sqrt{8-4}=8-10 \\ \rightarrow\sqrt{4}=-2 \\ \rightarrow2\ne-2 \\ \\ \rightarrow\sqrt{13-4}=13-10 \\ \rightarrow\sqrt{9}=3 \\ \rightarrow3=3 \end{gathered}[/tex]
Therefore, we can conclude that the solution is:
[tex]x=13[/tex]
