To answer this question we will use the following property:
[tex](\sqrt[]{a})^2=a\text{.}[/tex]
Adding 6 to the given equation we get:
[tex]\begin{gathered} \sqrt[]{2x+10}-6+6=2+6, \\ \sqrt[]{2x+10}=8. \end{gathered}[/tex]
Taking the above equation to the power of 2 we get:
[tex](\sqrt[]{2x+10})^2=8^2\text{.}[/tex]
Therefore:
[tex]2x+10=64.[/tex]
Subtracting 10 from the above equation we get:
[tex]\begin{gathered} 2x+10-10=64-10, \\ 2x=54. \end{gathered}[/tex]
Finally, dividing the above equation by 2 we get:
[tex]\begin{gathered} \frac{2x}{2}=\frac{54}{2}, \\ x=27. \end{gathered}[/tex]
Answer: x=27.
