Question

Solve

Answer 1

\(\sqrt {x+\sqrt2x}=\sqrt2x\)

Answer 2

square everything first

Answer 3

I know I need to do that, but I can't remember for the life of me what it does..... :/

Answer 4

\[\sqrt{x} = x ^{\frac{ 1 }{ 2 }}\]

Answer 5

how did you get that?

Answer 6

oh never mind lol

Answer 7

so \[(\sqrt{x})^{2} = x ^{1/2 *2} = x ^{\frac{ 2 }{ 2 }} = x\]

Answer 8

okay....what do I do next?

Answer 9

That is the property you need, so squaring both sides of your question ...

Answer 10

\[x + \sqrt{2}*x = 2 *x ^{2}\]

Answer 11

okay

Answer 12

so now you can rearrange things to make it easier to solve for x

Answer 13

First put all the x terms on one side

Answer 14

\(2x^2+x+ \sqrt 2x=0?\)

Answer 15

close, but remember your signs, you are subtracting those from both sides

\[2x ^{2} - x - \sqrt{2}*x = 0\]

Answer 16

whoopsies! lol

Answer 17

now, you see every term has a common factor x in it, factor an x out of each term

Answer 18

\(x(2x- \sqrt 2)\)?

Answer 19

close again, you forgot the -1 for the -x term

\[x*(2x - 1 - \sqrt{2}) = 0\]

Answer 20

so with this now, recall if you have two quantities equal to zero, you can set up two equations

Answer 21

x = 0

AND

\[2x - 1 - \sqrt{2} = 0\]

Answer 22

if either of those are true, the equations holds 0*a = 0

Answer 23

so the final answer:

x = 0 or \[x = \frac{ \sqrt{2} + 1 }{ 2 }\]

Answer 24

Okay thank you. I'm sorry it took so long....my mom had me go do something