We have a right triangle and two of its sides: one leg and the hypotenuse. In order to find the remaining side we can use the pythagorean theorem. For a right triangle with legs a and b and hypotenuse c we have:
[tex]c=\sqrt[]{a^2+b^2}[/tex]
Using this in our question we get:
[tex]\begin{gathered} 9=\sqrt[]{5^2+x^2} \\ 9=\sqrt[]{25+x^2} \end{gathered}[/tex]
So the equation to be used to find the missing length is:
[tex]9=\sqrt[]{25+x^2}[/tex]
In order to find x we can square both sides of that equation:
[tex]\begin{gathered} 9^2=(\sqrt[]{25+x^2})^2 \\ 81=25+x^2 \end{gathered}[/tex]
Then we substract 25 from both sides:
[tex]\begin{gathered} 81-25=25+x^2-25 \\ 56=x^2 \end{gathered}[/tex]
And we apply a square root to both sides:
[tex]\begin{gathered} \sqrt{56}=\sqrt{x^2} \\ x=\sqrt[]{56} \end{gathered}[/tex]
And that's the value of x.
