Question

(√x+10 ) + (√x-6) = 8 pls show work

Answer 1

Add like terms

Answer 2

2 sqrt[x]+10-6

Answer 3

2 sqrt[x]+4=8
2 sqrt[x]=4
(sqrt[x])^2=(2)^2
x=4

Answer 4

littleice, is this the problem you need help with ?

Answer 5

i know the answer comes to 15

Answer 6

yes thanks

Answer 7

let me ask you something first

is it \[\sqrt x +10\]

or

\[\sqrt{x+10}\]

Answer 8

\[\sqrt{x+10}+\sqrt{x-6}=8\]

Answer 9

okay,
so our main goal is to get rid of the square roots.

but before we proceed, there are things that you want
to always remember about eqn.s that involves sqrt.

it is that there are x's that are not allowed to use.

since te number inside the radical has to be positive,
first we have to note that

x>-10 and x>6

Answer 10

i thought it was x cant equal -10 or 6?

Answer 11

if we get an answer that doesn't fall in this category, then there are no solutions.

another thing that you have to do, (I'm not going to go into the detail unless you want to) is to check the answers when you get it.

the gist of the reason has to do with the fact that\[x^2=k, means, x= \pm \sqrt{k}\]

Answer 12

-10 and 6 are actually ok.

because sqrt(0) = 0

but sqrt(x) when x<0, becomes and imaginary number

Answer 13

k

Answer 14

alright let's proceed

Answer 15

when you get rid of sqrt.s you want to square them.

but when you square both sides just as it is, you will
end up having a square root again, so to avoid that,
you will isolate one of the terms that has a square root
around it, and deal with that first.

as follows

Answer 16

\[(\sqrt{x+10})^2 = (8-\sqrt{x-6})^2\]

so\[x+10 = 64 +16\sqrt{x-6}+(x-6)\]

Answer 17

now you only have one square root, so you isolate it
and then square both sides again

\[({x + 10 -64 -x +6 \over 16})^2 = \sqrt{x-6}^2\]

Answer 18

that way you will have a quadratic eqn. and
you know how to solve it from there.

don't forget to check the solutions, by plugging them in
because sometimes they will fail.

Answer 19

\[(-3 )^2= \sqrt(x-6)^2\]

is what you will get when you simplify the above

so 9 = x -6

thus x =15

Answer 20

however, let's see what happens when we plug this back in
into the original eqn.

sqrt(15+10)+sqrt(15-6) =5+3 =8

which actually works.

now we can guarantee that x =15.

Answer 21

did it help at all ?

Answer 22

idk what went thru my head but i got confused on how u did it did it a weird way and got the answer aswell

Answer 23

oh... ok :(
let me know if you need any explanations though :)

Answer 24

heres how i did it
\[\left( \sqrt{x+10} \right)^{2} = (8-\sqrt{x-6})^{2}\]
\[x+10=64+16\sqrt{x-6} + \sqrt{x-6}\]
\[x+10-64-x-6=16\sqrt{x-6}\]
\[48^{2}=(16\sqrt{x-6})^{2}\]
2304=256x-6
2304/256=x-6
9=x-6
15=x

Answer 25

it is the same thing

Answer 26

I just divided 16 on both sides first