Question

I don't know how to do this. Solve the equation. Identify any extraneous solutions. x= square root x +30

Answer 1

\[x=\sqrt{x+30}\]
\[x^2=x+30\]\[x^2-x-30=0\] solve the quadratic

Answer 2

How do you solve a quadratic?

Answer 3

this one factors as
\[(x-6)(x+5)=0\] so \(x=6\) or \(x=-5\)
then check the original equation
you will see that \(6\) works and \(-5\) does not

Answer 4

so what is the extraneous idk what that means

Answer 5

it means the one that doesn't work

Answer 6

6 works because
\[6=\sqrt{6+30}\]
\[6=\sqrt{36}\]\[6=6\] is true

Answer 7

oh thanks

Answer 8

-5 does not work because
\[-5\neq \sqrt{-5+30}\]
\[-5\neq \sqrt{25}\]
\[-5\neq 5\]

Answer 9

yw

Answer 10

oh see i didn't know that was how it works