## Compgroupmail 3 years ago help solve 1/2X=-1+sqrt(x-2)

1. Compgroupmail

correction $\frac{ 1 }{ 2 }x=-1 +\sqrt{x+2}$

2. SheldonEinstein

What you tried yet @Compgroupmail ?

3. Compgroupmail

I tried to bring it to the power by $\frac{ 1 }{ 4 }x=1+(x+2)$ /is this correct?

4. SheldonEinstein

see (a+b)^2 is NOT equal to a^2 + b^2 only. $\large{(\frac{1X}{2})^2 = (-1 + \sqrt{x-2})^2 }$ $\large{\frac{x^2}{4} = 1 + x-2 - 2\sqrt{x-2} }$

5. SheldonEinstein

Oh wait in your corrected question it is x+2 not x-2 so it will be : $\large{\frac{x} = 1+x-2 -2\sqrt{x+2}}$

6. SheldonEinstein

$\large{\frac{x^2}{4} = 1+x-2 -2\sqrt{x+2}}$

7. Compgroupmail

ok but I still don't understand how you broke it down to that. Can we go through it step by step?

8. SheldonEinstein

Oh! Sorry I think I confused you, yes why not... so do you know the identity of (a+b)^2 = ?

9. Compgroupmail

a^2+2ab+b^2

10. SheldonEinstein

Right! so in RHS (Right hand side) we have : -1 + sqrt{x+2} , correct?

11. Compgroupmail

left side of equation $(\frac{ 1 }{ 2 }x)^2= \frac{ 1 }{ 4 }x$. Correct?

12. Compgroupmail

right. That is the right hand side. What's next?

13. SheldonEinstein

Yes , so square the right hand side ... that is : $\large{( \sqrt{x+2} - 1 )^2 }$ Can you square that?

14. Compgroupmail

no. Not 100% how to do it. That's what's messing me up.

15. SheldonEinstein

Wait for 1 minute, I am opening google chrome as IE is quite slow

16. Compgroupmail

ok no problem

17. Algebraic!

add 1 to both sides and square both sides $(\frac{ x }{ 2 } +1)^2 = x +2$

18. Algebraic!

$\frac{ x^2 }{4 } +x +1 = x+2$

19. Algebraic!

x^2 =4

20. Compgroupmail

ahh. I understand now :) THanks!