How do you solve $(2x)^(1/2)=x-4$ ?

Question

1310 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-22T16:50:13

${8}$

You're going to want to get rid of the 1/2 exponent. You can do this by squaring both sides.

$((2x)^(1/2))^2 = (x - 4)^2$

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

$2x = x^2 - 4x - 4x + 16$

$0 = x^2 - 10x + 16$

$0 = (x - 8)(x - 2)$

$x = 8 and 2$

This is a rational equation, so extraneous solutions are always a possibility, if not a likelihood. Always check your solutions.

$(2 * 2)^(1/2) =^? 2 - 4$

$sqrt(2) != -2 color(red)(xx)$

$(2 * 8)^(1/2) =^? 8 - 4$

$sqrt(16) = 4$

The only valid solution is $x = 8$ .

Hopefully this helps!

How do you solve (2x)^(1/2)=x-4(2x)^(1/2)=x-4?