Question 60809
{{{sqrt(a+7)=1+sqrt(2a)}}}
{{{(sqrt(a+7))^2=(1+sqrt(2a))^2}}}
{{{a+7=(1+sqrt(2a))(1+sqrt(2a))}}}
{{{a+7=1+2sqrt(2a)+2a}}}
{{{a-2a+7-1=1-1+2sqrt(2a)+2a-2a}}}
{{{-a+6=2sqrt(2a)}}}
{{{(-a+6)^2=(2sqrt(2a))^2}}}
{{{(-a+6)(-a+6)=2^2(2a)}}}
{{{a^2-12a+36=4(2a)}}}
{{{a^2-12a+36=8a}}}
{{{a^2-12a-8a+36=8a-8a}}}
{{{a^2-20a+36=0}}}
(a-2)(a-18)=0
a-2=0  and a-18=0
a=2 and a=18  Check for extraneous solutions:
{{{sqrt(2+7)=1+sqrt(2(2))}}}
{{{sqrt(9)=1+sqrt(4)}}}
{{{3=1+2}}}
{{{3=3}}}  a=2 is a valid solution.
{{{sqrt(18+7)=1+sqrt(2(18))}}}
{{{sqrt(25)=1+sqrt(36)}}}
{{{5=1+6}}}
{{{5=7}}}  a=18 is extraneous.
The only valid solution is a=2.
Happy Calculating!!!