We need to solve:
[tex]\sqrt{x-5}+\sqrt{x}=5[/tex]
One way of solving it is by writing the terms on the left side as integers that add up to 5:
[tex]\begin{gathered} 0+5=5 \\ \\ 1+4=5 \\ \\ 2+3=5 \end{gathered}[/tex]
Notice that the value of the first term must be less than the value of the second since the number inside the first root is the number inside the second less 5.
Now, we can check if both terms imply the same value for x:
[tex]\begin{gathered} \sqrt{x-5}=0\Rightarrow x=5 \\ \sqrt{x}=5\Rightarrow x=25 \end{gathered}[/tex][tex]\begin{gathered} \sqrt{x-5}=1\Rightarrow x=6 \\ \sqrt{x}=4\Rightarrow x=16 \end{gathered}[/tex][tex]\begin{gathered} \sqrt{x-5}=2\Rightarrow x=9 \\ \sqrt{x}=3\Rightarrow x=9 \end{gathered}[/tex]
Therefore, for x = 9, we have:
[tex]\sqrt{x-5}+\sqrt{x}=\sqrt{9-5}+\sqrt{9}=\sqrt{4}+\sqrt{9}=2+3=5[/tex]
Answer: x = 9
