Question

\[\sqrt{6x-17}=4-x\]

Answer 1

im soooooooo lost

Answer 2

square both sides

Answer 3

it should be clear what you get on the left, because when you square the square root of something, you just get the something

Answer 4

so if you square both sides you get \(6x-17\) on the left. on the right you get
\((4-x)^2=(4-x)(4-x)=16-8x+x^2\)

Answer 5

now your job is to solve
\[6x-17=16-8x+x^2\] which is a quadratic equation.
do you know how to solve it?

Answer 6

no im flipping lost

Answer 7

if so then you are in good shape.
if not, you are stuck
put everything on one side of the equal sign to get
\[x^2-14x+33=0\]

Answer 8

hold the phone

were the first steps clear or were they confusing?

Answer 9

no im confused this pellet is killing my brain

Answer 10

lets start at the beginning. this is what you started with
\[\sqrt{6x-17}=4-x\]

Answer 11

okay so there is no solution yes that is the equation

Answer 12

you have to eliminate the square roots

Answer 13

and you do that by squaring both sides

Answer 14

when you square
\[\sqrt{6x-17}\] you get
\[6x-17\] right?

Answer 15

like if i square \(\sqrt{5}\) i get 5

Answer 16

the only algebra you need to do at this step is square the right hand side, which was
\[4-x\] and when you compute
\[(4-x)^2\] you get
\[(4-x)(4-x)=16-8x+x^2\] is that confusing or is it ok?

Answer 17

there is a solution
you have to solve
\[6x-17=16-8x+x^2\] or
\[x^2-14x+33=0\]
\[(x-3)(x-11)=0\]
\[x=3\] or
\[x=11\] so those are the possible answers. now you have to check them

Answer 18

when you do you will see that 11 does not work, but that 3 does

Answer 19

well im still lost im sorry im mathematically challenged

Answer 20

go slow
don't try to do it all at once
this one take several steps, but i think i have written them all out