How do you solve $sqrt(x+6)-2=sqrt(x-2)$ ?

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Answer 1 · 2016-04-29T19:41:05

$x=3$

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Square both sides

$(sqrt(x+6)-2)^2=x-2$

$(cancel(x)+6) -4sqrt(x+6)+4=cancel(x)-2$

$10-4sqrt(x+6)=-2$

$4sqrt(x+6)=12$

$sqrt(x+6)=3$

square both sides

$x+6=9$

$x=3$

How do you solve sqrt(x+6)-2=sqrt(x-2)sqrt(x+6)-2=sqrt(x-2)?