Find the non-extraneous solutions of the square root of the quantity x plus 9 minus 5 equals quantity x plus 4.

x = −2
x = −9 and x = −2
x = 9
x = −9 and x = −8

Question

Find the non-extraneous solutions of the square root of the quantity x plus 9 minus 5 equals quantity x plus 4.

 x = −2
 x = −9 and x = −2
 x = 9
 x = −9 and x = −8

princesssleelee · Answer

$$\sqrt{x+9}-5=x+4$$

princesssleelee · Answer

I found out that the two x's however equal -2 and -26, if i did the math correctly.

princesssleelee · Answer

-36, not -26, sorry.

princesssleelee · Answer

no, it doesnt.

mathstudent55 · Answer

$\sqrt{x + 9} - 5 = x + 4$

Add 5 to both sides.

mathstudent55 · Answer

Then square both sides.

solomonzelman · Answer

non-extraneous solution:
The solution that works in the original equation.

extraneous solution:
The solution that is the result of (correct) work/transformations,
but that does not work in the initial equation.

(definitions, just in case)

mathstudent55 · Answer

$\sqrt{x + 9}  = x + 9$

$(\sqrt{x + 9})^2  = (x + 9)^2$

princesssleelee · Answer

I got past that part

solomonzelman · Answer

can you post the work that you have please?

mathstudent55 · Answer

$x + 9 = x^2 + 18x + 81$

princesssleelee · Answer

then subtract x

mathstudent55 · Answer

$x^2 + 17x + 72 = 0$

princesssleelee · Answer

eventually getting x=-2 and x=-36

princesssleelee · Answer

I passed all of that, and thats what I got

mathstudent55 · Answer

2 and 36 do not add to 17, so that is incorrect.
You need to factor the left side correctly.

mathstudent55 · Answer

$x^2 + 17x + 72 = 0$

At this point, you can try factoring the left side.
What two numbers have a product of 72 and a sum of 17?

princesssleelee · Answer

Now i am completely lost. I did not add 17

mathstudent55 · Answer

$x^2 + 17x + 72 = 0$

mathstudent55 · Answer

Wait a minute. 
Let's see where your error starts. 
Did you get the equation I got?

princesssleelee · Answer

I am going to try and upload a photo of my work from where we were on the same page

mathstudent55 · Answer

Ok

princesssleelee · Answer

Sorry, it is sloppy and i wasnt planning on sharing lol

princesssleelee · Answer

I will also share the example that I have in my notes.

mathstudent55 · Answer

Starting with the last line as line 1, go up to line 6.

You have

$0 = x^2 + 17x + 72$

You have the correct equation.
Ok?

mathstudent55 · Answer

Your work is very clear. No problem there.

mathstudent55 · Answer

Your error is on a line below where you tried to factor the quadratic.

princesssleelee · Answer

What was the error

princesssleelee · Answer

attachment

mathstudent55 · Answer

You factored like this:

$(x + 2)(x + 36) $

If you multiply it out (using FOIL), you get this:

$= x^2 + 36x + 2x + 72$

$= x^2 + 38x + 72$

As you can see this is not the quadratic you started with.

princesssleelee · Answer

what did I start with?

mathstudent55 · Answer

You started wit the quadratic you wanted to factor:

$x^2 + 17x + 72$

mathstudent55 · Answer

Ok. Now we know that your factoring is not correct since it does not multiply out back to the quadratic trinomial you had originally.

mathstudent55 · Answer

Your factoring is of this type:
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