Question 314753
{{{x=1+6sqrt(x-9)}}}
<pre><b>
Isolate the radical term on the right

{{{x-1=6sqrt(x-9)}}}

Square both sides:

{{{(x-1)^2=(6sqrt(x-9))^2}}}

{{{(x-1)(x-1)=36(x-9)}}}

{{{x^2-x-x+1=36x-324}}}

{{{x^2-2x+1=36x-324}}}

{{{x^2-38x+325=0}}}

{{{(x-25)(x-13)=0}}}

x-25=0       x-13=0
   x=25         x=13

Checking x=25

{{{x=1+6sqrt(x-9)}}}
{{{25=1+6sqrt(25-9)}}}
{{{25=1+6sqrt(16)}}}
{{{25=1+6*4}}}
{{{25=1+24}}}
{{{25=25}}}

So x=25 is a solution.

Checking x=13

{{{x=1+6sqrt(x-9)}}}
{{{13=1+6sqrt(13-9)}}}
{{{13=1+6sqrt(4)}}}
{{{13=1+6*2}}}
{{{13=1+12}}}
{{{13=13}}}

So x=13 is also a solution.

Edwin</pre>