Question 912823
{{{sqrt(2x)+5=x+1}}}
{{{sqrt(2x)=x-4}}}
{{{x-sqrt(2)sqrt(x)-4=0}}}
Let {{{u=sqrt(x)}}},
{{{u^2-sqrt(2)u-4=0}}}
Factoring,
{{{(u+sqrt(2))(u-2sqrt(2))=0}}}
Two solutions:
{{{u+sqrt(2)=0}}}
{{{u=-sqrt(2)}}}
{{{sqrt(x)=-sqrt(2)}}}
This does not lead to a solution in {{{x}}}.
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{{{u-2sqrt(2)=0}}}
{{{u=2sqrt(2)}}}
{{{u=sqrt(8)}}}
{{{sqrt(x)=sqrt(8)}}}
{{{highlight(x=8)}}}