1. random231

|dw:1441477010872:dw| now square both sides and solve the eqn

2. Jhannybean

$2\sqrt{4}-2x=2-x$ Rearrange.$2\sqrt{4}-2=2x-x$$\boxed{x=2\sqrt{4}-2}$

3. IrishBoy123

$\sqrt{4}$ is this for real?!

4. anonymous

No, I think it's four real xD im sorry i had to

5. Jhannybean

You didnt simplify my answer? :(

6. IrishBoy123

it's "four real" !!! lol!!

7. anonymous

jhannybean, the 2x is also the under the radical. so can we really send it to the other side ?

8. Jhannybean

so your function is $$2\sqrt{4-2x}= 2-x$$?

9. anonymous

yeah

10. Jhannybean

Okay. Then we would have to begin by squaring both sides. OUr goal is to isolate the x's to one side.

11. Jhannybean

$(2\sqrt{4-2x})^2 = (2-x)^2$$4(4-2x) = 4-4x+x^2$$16-8x=4-4x+x^2$$x^2-4x+8x=16-4$$x^2+4x-12=0$Can you factor this now?

12. anonymous

um is it (x + 2)(x - 6) = 0 ?

13. Jhannybean

$(x+2)(x-6) = x^2 -4x-12 \ne x^2+4x-12$

14. anonymous

oh i think i got it is it (x - 2)( x + 6 ) ?

15. Jhannybean

Yep

16. anonymous

then we simplify like this : x - 2 = 0 x = 2 and x + 6 = 0 x = - 6 so the answer is x = 2, -6

17. Jhannybean

Mmhmm

18. anonymous

omg thank you so much :)

19. Jhannybean

No problem :)

20. anonymous

can i ask u one more question ?

21. Jhannybean

Sure

22. anonymous

it is similar, $\sqrt{5x - x } = 0$

23. anonymous

how do we solve this ?

24. anonymous

Square both sides first, right?

25. Jhannybean

Again, we want to isolate x so we need to square both sides. Same method.

26. anonymous

wouldnt it just be like 4x = 0 at the end? xD or just plain out 0?

27. Jhannybean

You are correct.

28. anonymous

Oooooooo, look at me im doin stuff xD

29. anonymous

oh sorry , made a mistake again i meant $\sqrt{5x} - x = 0$

30. anonymous

Wouldnt that be the same outcome?

31. anonymous

Er... nevermind

32. Jhannybean

$\sqrt{5x}-x=0$$\sqrt{5x}=x$$(\sqrt{5x})^2=x^2$$5x=x^2$$x^2-5x=0$$x(x-5)=0$$x=0$$x-5=0 \iff x=5$

33. Jhannybean

@BweadedChicken no, not the same outccome.

34. anonymous

oh that was it ? i thought we need to complete the square and all any way , thank you you're the best :)

35. Jhannybean

Yeah, completing the square comes along with complex quadratic functions that need to be simplified. You'll know when you see them.

36. anonymous

oh ok :)