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# solve for x

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Hi good people!!!....

The sum is:

$$x-3 \sqrt{x+2}=2$$

when we solve x, we get x=14 or x=-1

-1 is rendered na, but 14, not---why is this?

If I replace x with -1, we get

$$-1-3 \sqrt{-1+2}=2$$

which is $$-4 \sqrt{1}=2$$

which is $$-4=2$$...which of course is NOT..

But the same goes for the 14??

$$14-3 \sqrt{14+2}=2$$

which is $$11 \sqrt{16}=2$$

which is $$44=2$$

which also is NOT???

all and any answer is very appreciated!..thank you all kindly.

Oct 12, 2020

#1
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-1` - 3 sqrt(-1+2)    = 2  ?????    no it does not...it equals  -4

the solutions you obtained are both incorrect...you made a mistake somewhere (we ALL do !)

......go back and solve it again to get different answers

Oct 12, 2020
#2
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Update :     I looked at it a little closer:

x-2  = 3 (sqrt(x+2))   square both sides

x^2 - 4x + 4   = 9 (x+2)

x^2 -13x -14  = 0

Quadratic equation shows x = -1   and 14

14 - 3 sqrt (14+2) = 2

14 - 3 (sqrt16) = 2             ( look at your step where you get    11 sqrt (16)   <---- this is where you made your error)

14 - 12 = 2                           so 14 IS an answer     only -1 is NOT.

Oct 12, 2020
edited by ElectricPavlov  Oct 12, 2020
edited by ElectricPavlov  Oct 12, 2020
#3
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aawww, you know what I did?????...I did not follow the order of operations when I checked the roots.....Thank you for your time, I do appreciate..

juriemagic  Oct 12, 2020
#4
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Hi Juriemagic,

It is really good to see you here. Oct 12, 2020