Question

Solve the radical, and check all proposed solutions:

Answer 1

\[\sqrt{18x-9}=x+4\]

Answer 2

Square both sides first. Let me know what you get

Answer 3

\[18x-9=x ^{2}+16\]

Answer 4

You squared the right side incorrectly

Answer 5

You were supposed to get

\[18x-9=(x+4)^2\]

Answer 6

Now, expand the right side.

Answer 7

18x-9=(x+4)(x+4)?

Answer 8

Okay, now multiply the right side.

Answer 9

x^2+8x+16

Answer 10

\[0=x ^{2}-10x+25\]

Answer 11

Okay, now factor the right side.

Answer 12

What happened?

Answer 13

It froze up..0=(x-5)(x-5)

Answer 14

Which is the same thing as

\[0 = (x-5)^2\]

Now take the square root of both sides.

Answer 15

What?

Answer 16

Do you know what a square root is?

Answer 17

Take the radical of both sides.

Answer 18

\[\sqrt{0} = \sqrt{(x-5)^2}\]

Answer 19

Don't tell me you've never seen that before.

Answer 20

Oh, Okay, I have, but it just looked wrong

Answer 21

Okay, so what is the result of that?

Answer 22

15?