Question

Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

square root of the quantity x plus 7 end quantity minus 1 equals x

Answer 1

nope-

Answer 2

um how would I do that?

Answer 3

oh so then minus 1 would be -1

Answer 4

what about the quantity though?

Answer 5

what about the quantity tho

Answer 6

what do I put for that?

Answer 7

ohhhhh that makes more sense

Answer 8

do we solve what's in the parenthesis first?

Answer 9

I think so?

Answer 10

oh so we had to remove them

Answer 11

so would I need a calculator?

Answer 12

so would we add 10 plus 25?

Answer 13

yeah

Answer 14

ohhh now I get it

Answer 15

wait so would I have to write the long version too?

Answer 16

do I just write down what the link steps are?

Answer 17

oh alright so I would write down solving it with the quadratic formula too

Answer 18

oh

Answer 19

ill just write down the steps it shows

Answer 20

test how?

Answer 21

oh so I plug it in

Answer 22

what do I do once I plug it in?

Answer 23

um

Answer 24

It's two entirely different questions with the 1 in and out

Answer 25

it's not correct, if you had -1 under the square root, it would be square root x + 6, if you had in outside however... you would first need to add 1 to both sides, THEN square

Answer 26

im very confused-

Answer 27

add 1 to both sides \[\sqrt{x+7} = x+1 \\x+7 = (x+1)^2\]

Answer 28

wait so who's right then

Answer 29

If I am looking and solving this correctly as snow goes. I would have to say snow is correct.

Answer 30

so the other guy was wrong? yikes

Answer 31

what would be the correct way to solve this then cus now im confused

Answer 32

"square root of the quantity x plus 7 end quantity minus 1 equals x"
think of the quantity and end quantity as parenthesis
square root of the quantity x plus seven, end quantity is \(\sqrt{x+7}\) then that minus 1, equals to x

Answer 33

then you get the equation \[\sqrt{x+7}-1=x\]

Answer 34

so I just type what you wrote

Answer 35

that would be the equation
do you know how to solve for x?

Answer 36

no

Answer 37

can you add 1 to both sides

Answer 38

so for 7 and 1?

Answer 39

can you add the left hand expression by 1, and the right by 1

Answer 40

oh so the 2 x's basically?

Answer 41

do you understand how I get from \(\sqrt{x+7}-1=x\)
to \(\sqrt{x+7}=x+1\)

Answer 42

we just add a one for each side

Answer 43

correct

Answer 44

now can you write out the equation you would get if you squared both sides?

Answer 45

would it be the same just fully squared? Orr

Answer 46

?

Answer 47

just write out what you think

Answer 48

I think it would look the same

Answer 49

\(\sqrt{x+7}=x+1\)
square both sides
\((\sqrt{x+7})^2 = (x+1)^2\)
correct?

Answer 50

im running out of time could you maybe just write out the steps for me please

Answer 51

\[x+7 = (x+1)^2\]
FOIL method: \((a+b)^2 = a^2 + 2ab+b^2\)

\[x+7=x^2 + 2x+1 \\ x^2 +x -6=0\\(x+3)(x-2)=0\]

Answer 52

I factored it for you, with this you will get two solutions

Answer 53

one is extraneous the other is the actual answer

one of them is extraneous because if you put it back into the original question, it won't go through the square root. so basically, hint the positive one is the answer, the negative is the extraneous solution

Answer 54

alright thanks