Question

k

Answer 1

are we solving for x here?

Answer 2

\[\sqrt{x+7}-x=1\]Right?

Answer 3

x will = 9

Answer 4

It says solve and to check for extraneous solutions.

And yes @SolomonZelman

Answer 5

\[\sqrt{x+7}-x=1\]\[\sqrt{x+7}-x\color{red} { +x }=1\color{red} { +x }\]\[\sqrt{x+7}=x+1\]square both sides\[(~\sqrt{x+7}~)\color{red} { ^2 }=(~x+1~) \color{red} { ^2 }\]\[x+7=x^2+2x+1\]so far so good?

Answer 6

Ahh okay. I'm following.

Answer 7

\[x+7\color{red} { -x }=x^2+2x+1\color{red} { -x }\]\[7=x^2+2x+1\]\[7\color{red} { -7 }=x^2+2x+1\color{red} { -7 }\]\[x^2+2x-6=0\]what about now?

Answer 8

Yes. It's a lot of steps, but it's helping me understand it better. What next??

Answer 9

can you do it now?

Answer 10

Well I'm not too sure. I had a few guesses what x was, but I don't think they're right. What would I do next? Sorry, I'm not too good at math.

Answer 11

Do we factor?

Answer 12

Sorry for not replying right away.

Answer 13

It's okay. Gave me time to look into the problem more. :)

Answer 14

\[\huge\color{blue}{ \frac{-b±\sqrt{b^2+4ac} }{2a} } \]

Answer 15

\[\huge\color{blue}{ \huge\color{red}{1}x^2+\huge\color{red}{2}x+\huge\color{red}{6}=0 } \]see the a b c ?
plug them into the quadratic formula.

Answer 16

\[-1 \pm \sqrt{-1 + 4*2*6} / 2*2\]

Answer 17

Like that?

Answer 18

Not exactly....

Answer 19

Then how would I do it??

Answer 20

Sorry your equation was\[x^2+2x-6=0\]

\[\huge\color{red}{ \frac{-2±\sqrt{ 1^2-4 \times 2 \times (-6)} }{2 \times 2} }\]

Answer 21

\[\huge\color{red}{ \frac{-2±\sqrt{49}}{4} }\]

Answer 22

\[\huge\color{red}{ \frac{-2±7}{4} }\]you tell me what the answers are....

Answer 23

@SolomonZelman those are what I got. Seems odd though.

Answer 24

Well, it's right though....

Answer 25

Really? Haha alright then. Thanks a bunch!