How do you solve $sqrt(x+7) = x + 1$ and find any extraneous solutions?

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Answer 1 · 2018-04-19T23:00:37

I tried this:

Let us square both sides:

$(sqrt(x+7))^2=(x+1)^2$

$x+7=x^2+2x+1$

rearrange:

$x^2+x-6=0$

$x_(1,2)=(-1+-sqrt(1+24))/2=(-1+-5)/2$

giving:

$x_1=-3$ that doesn't work;
$x_2=2$ .

How do you solve sqrt(x+7) = x + 1sqrt(x+7) = x + 1 and find any extraneous solutions?