How do you solve $sqrt(x+2) = x-4$ ?

Question

1614 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-10T23:01:49

$x=7$

First square both sides of the equation, noting that this may introduce spurious solutions:

$x+2 = (x-4)^2 = x^2-8x+16$

Subtract $x+2$ from both ends to get:

$0 = x^2-9x+14 = (x-2)(x-7)$

So $x=2$ or $x=7$

If $x=2$ then $sqrt(x+2) = sqrt(4) = 2 != -2 = 2 - 4 = x-4$

If $x=7$ then $sqrt(x+2) = sqrt(9) = 3 = 7-4 = x-4$

So $x=7$ is the only valid solution of the original equation.

How do you solve sqrt(x+2) = x-4sqrt(x+2) = x-4?