How do you solve $sqrt (x+2) +4 = x$ and find any extraneous solutions?

Question

1241 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-06T11:50:01

$color(maroon)("Solutions : " x = 2, 7$

$sqrt(x+2) + 4 = x$

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

Squaring both sides, $x + 2 = (x -4)^2$

$x + 2 = x^2 - 8x + 16$

$x^2 -9x + 14 = 0$

$x^2 - 2x - 7x + 14 = 0$

$x(x - 2) - 7 (x - 2) = 0$

$(x - 2) * (x - 7) = 0$

$x = 2, 7$

How do you solve sqrt (x+2) +4 = xsqrt (x+2) +4 = x and find any extraneous solutions?