solve 5+square root x+2 = 8+ square root x-7
note; the x+2 and x-7 are under the square root sign

Question

solve 5+square root x+2 = 8+ square root x-7
note; the x+2 and x-7 are under the square root sign

hartnn · Answer

subtract 5 from both sides first, what do u get ?

anonymous · Answer

$$\sqrt{x+2} = 3 + \sqrt{x-7}$$

hartnn · Answer

now square both sides! 
notice that one of the square root (on left) gets eliminated! :)

anonymous · Answer

so my answer is $$3 + \sqrt{x-7}$$?

anonymous · Answer

wait.. if that's squared it'd 3+x-7

hartnn · Answer

no....the entire left side does not get eliminated, only the square root part,
what do u get after you square both sides of that ?

anonymous · Answer

x+2=3+x-7?

hartnn · Answer

on the right side, the form is a+b
and its square will be a^2+2ab+b^2
so now whats the square of 3 + sqrt (x-7) ??

anonymous · Answer

3^2+x-7

hartnn · Answer

nopes, there will be 3 terms 
a^2
b^2
2ab

here a = 3
b=sqrt(x-7)

anonymous · Answer

okay so.. it'll be \[3^{2}+\sqrt{x-7}^{2}+2(3)(\sqrt{x-7})

anonymous · Answer

that didn't work very well... $$3^{2}+\sqrt{x-7}^{2}+2(3)(\sqrt{x-7})$$

hartnn · Answer

but thats correct,
you just need to simplify the terms.

anonymous · Answer

$$9+\sqrt{x ^{2}-7^{2}} + \sqrt{6x-42}$$ Like that?

hartnn · Answer

note $\sqrt {stuff^2}=stuff$

hartnn · Answer

and last term is just $6 \sqrt{x-7} $

anonymous · Answer

$$9+x-7 +6\sqrt{x-7}$$

hartnn · Answer

yes, simplify that

anonymous · Answer

$$2+x+6\sqrt{x-7}$$ can whats in the sqrt simplify?

hartnn · Answer

and on the left side we had 
x+2 
so, try to isolate sqrt (x-7) from 
$x+2=2+x+6\sqrt{x-7}$

hartnn · Answer

still there ?

anonymous · Answer

yes

hartnn · Answer

goo , so what gets cancelled?

hartnn · Answer

**good

anonymous · Answer

the 9 and -7 get combined to 2

hartnn · Answer

we are simplifying this, right ? 
$x+2=2+x+6\sqrt{x-7}$
the x+2 gets cancelled, what remains ?

anonymous · Answer

only the $$6\sqrt{x-7}$$ is left isn't it?

hartnn · Answer

yes! but on the left side there's a 0 
so, 
0=6 sqrt {x-7}
square both sides, what do u get ?

anonymous · Answer

you can't change 0 by squaring it so $$0 = 6(x-7)$$ is that what you get?

hartnn · Answer

0 = 36 (x-7)
but the point is, that 
x-7 = 0 !!
got this ?
so what's x ?

hartnn · Answer

it would be easy to figure out that x-7=0 gives you x=7 
ask if any doubts in any steps :)

anonymous · Answer

oh okay so my final answer is x=7?

hartnn · Answer

yes! :)

hartnn · Answer

you can verify it by plugging in x=7 in your original equation...

anonymous · Answer

Awesome! Thank you very much for helping me! I'm not good at math at all.. so I always appreciate it when people take the time to help me :)

hartnn · Answer

you are most welcome ^_^
with enough practice, you can become better at math than me !! :P good luck! :)

anonymous · Answer

Thanks again :)