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If (x - 3)^2 = 225, which of the following could be the

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If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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New post 24 Feb 2013, 16:57
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If (x - 3)^2 = 225, which of the following could be the value of x + 3 ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have\(x - 3= 15\)so why the explanation says: \(x - 3 = 15\) and \(x - 3 = -15\) ????? :help2

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Re: If (x - 3)^2 = 225, which of the following could be  [#permalink]

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New post 24 Feb 2013, 21:03
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carcass wrote:
If \((x - 3)^2 = 225\), which of the following could be the value of \(x + 3\) ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have\(x - 3= 15\)so why the explanation says: \(x - 3 = 15\) and \(x - 3 = -15\) ????? :help2


Honestly carcass, that's a newbie mistake and you should not be making it!

\((x - 3)^2 = 15^2\)

When you take the root, you get
|x-3| = 15
and hence you get x = 18 or -12

Alternatively,
\((x - 3)^2 - 15^2 = 0\)
(x - 3 - 15)(x - 3 + 15) = 0
x = 18 or -12
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Re: If (x - 3)^2 = 225, which of the following could be  [#permalink]

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New post 24 Feb 2013, 18:14
carcass wrote:
If \((x - 3)^2 = 225\), which of the following could be the value of \(x + 3\) ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have\(x - 3= 15\)so why the explanation says: \(x - 3 = 15\) and \(x - 3 = -15\) ????? :help2


both 18 and -12 satisfy the given equation

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Re: If (x - 3)^2 = 225, which of the following could be  [#permalink]

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New post 24 Feb 2013, 18:23
jbisht wrote:
carcass wrote:
If \((x - 3)^2 = 225\), which of the following could be the value of \(x + 3\) ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have\(x - 3= 15\)so why the explanation says: \(x - 3 = 15\) and \(x - 3 = -15\) ????? :help2


both 18 and -12 satisfy the given equation

Posted from my mobile device


hence, x+3 is 21 or -9

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Re: If (x - 3)^2 = 225, which of the following could be  [#permalink]

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New post 24 Feb 2013, 19:01
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Re: If (x - 3)^2 = 225, which of the following could be  [#permalink]

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New post 24 Feb 2013, 19:44
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carcass wrote:
If \((x - 3)^2 = 225\), which of the following could be the value of \(x + 3\) ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have\(x - 3= 15\)so why the explanation says: \(x - 3 = 15\) and \(x - 3 = -15\) ????? :help2


Yes here are my two cents...

\((x - 3)^2 = 225\)

Since squaring on both sides leaves +/- \(x - 3 = +/- 15\)
This gives two eqns..
\(x - 3 = 15\)
\(x - 3 = -15\)

So, x= 18 means x+3=15
or
x=-12 means x+3=-9
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Re: If (x - 3)^2 = 225, which of the following could be  [#permalink]

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New post 25 Feb 2013, 02:46
1
VeritasPrepKarishma wrote:
carcass wrote:
If \((x - 3)^2 = 225\), which of the following could be the value of \(x + 3\) ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have\(x - 3= 15\)so why the explanation says: \(x - 3 = 15\) and \(x - 3 = -15\) ????? :help2


Honestly carcass, that's a newbie mistake and you should not be making it!

\((x - 3)^2 = 15^2\)

When you take the root, you get
|x-3| = 15
and hence you get x = 18 or -12

Alternatively,
\((x - 3)^2 - 15^2 = 0\)
(x - 3 - 15)(x - 3 + 15) = 0
x = 18 or -12



No no .......you are perfectly right :(.

maybe tired maybe stressed..........I know but you are right. Thanks
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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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New post 27 Feb 2014, 20:16
One more method (This is time consuming)

Writing the equation as

x^2 - 6x + 9 - 225 = 0

x^2 - 6x + 9 - 216 = 0

(x-18) . (x+12) = 0

x = 18 OR x = -12

x+3=15 or x+3 = -9
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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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New post 23 Aug 2016, 06:58
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If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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New post Updated on: 03 Nov 2016, 06:13
x-3 = 15

or

x-3= -15



So x=18 or x=-12

x+3=21 or x+3=-9

So Answer B
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Originally posted by AnisMURR on 03 Nov 2016, 03:48.
Last edited by AnisMURR on 03 Nov 2016, 06:13, edited 1 time in total.
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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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New post 03 Nov 2016, 04:05
How we can confirm which answer to be considered?

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If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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New post 03 Nov 2016, 04:15
Pm091989 wrote:
How we can confirm which answer to be considered?

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(x-3)^2= 225
(x-3)^2= 15^2
(x-3)= +15 or -15
x=18 or -12
now the question asks which could be the value of x+3
if x=18 ==> x+3=21 (could be)
if x=-12==> x+3= -9 (could be)

only-9 is available as an option.
If both -9 and 21 were available as individual options then the question would be wrong.
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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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New post 03 Nov 2016, 11:33
carcass wrote:
If (x - 3)^2 = 225, which of the following could be the value of x + 3 ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18

in this question if we take the square of both sides we have\(x - 3= 15\)so why the explanation says: \(x - 3 = 15\) and \(x - 3 = -15\) ????? :help2


\(\sqrt{(x - 3)^2} = \sqrt{225}\)

Or, \(( x - 3 ) =\) + \(15\)

If x = +15

x - 3 = 15

Or, x = 18 so x + 3 = 21

If x - 3 = - 15

Or, x = -12 , so x + 3 = -9

Hence, answer will be (C) -9
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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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New post 04 Nov 2016, 16:18
carcass wrote:
If (x - 3)^2 = 225, which of the following could be the value of x + 3 ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18


We can start by taking the square root of both sides of the equation (x - 3)^2 = 225.

√(x - 3)^2 = √225

x - 3 = 15 or x - 3 = -15

Thus, x = 18 or -12.

So possible values of x + 3 are as follows:

18 + 3 = 21

-12 + 3 = -9

Since -9 is the only answer within the answer choices, the answer is C.

Answer: C
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Re: If (x - 3)^2 = 225, which of the following could be the  [#permalink]

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New post 04 Nov 2016, 22:28
carcass wrote:
If (x - 3)^2 = 225, which of the following could be the value of x + 3 ?

(A) -15
(B) -12
(C) -9
(D) 15
(E) 18


(x - 3)^2 = 225
i.e. x-3 = +15 or -15
i.e. x = +18 or -12
i.e. x+3 = +21 or -9

Answer: option C
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