How do you solve $sqrt(u+6)=u$ and check your solution?

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Answer 1 · 2017-07-13T19:48:05

$u=3$

$sqrt(u+6) = u$

$u+6=u^2$ $->$ square both sides to get rid of radical

$0=u^2 - u - 6$ $->$ subtract $6$ and $u$ to bring all terms to one side

$0=(u-3)(u+2)$ $->$ factor

There are two possibilities:

$0=u-3$
$=>u=3$

$0=u+2$
$=>u=-2$

To check your solutions, substitute them back into the original equation.

$u=3$

$sqrt(u+6)=u$
$sqrt(3+6)=3$
$sqrt(9)=3$
$3=3$ $->$ works

$u=-2$

$sqrt(u+6)=u$
$sqrt(-2+6)=-2$
$sqrt(4)=-2$
$2=-2$ $->$ does not work

So, the only solution is $u=3$ .

How do you solve sqrt(u+6)=usqrt(u+6)=u and check your solution?