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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

problem solving

by BTGmoderatorRO » Thu Nov 02, 2017 11:51 am

If (x + 2)^2 = âˆ’ 4 + 10x , then which of the following could be the value of x?

A) 2
B) 1
C) 0
D) âˆ’1
E) âˆ’2
OA is a
Can anyone help me with the solution to this question? Thank you for your help

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Source: Beat The GMAT — Problem Solving | Thu Nov 02, 2017 11:51 am

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by [email protected] » Thu Nov 02, 2017 1:23 pm

Hi Roland2rule,

While this question can be solved Algebraically, we're told that one of the numbers IS a solution to the equation - so we can also solve it by TESTing THE ANSWERS. Once we find an answer that 'fits', we can stop working.

Let's start with [spoiler]Answer A: 2... IF X=2, then we have (4)^2 = -4 +2(10).... 16 = 16. Since the equation 'balances', this must the answer.[/spoiler]

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Thu Nov 02, 2017 4:50 pm

If (x + 2)^2 = - 4 + 10x , then which of the following could be the value of x?

A) 2
B) 1
C) 0
D) -1
E) -2
OA is a
Can anyone help me with the solution to this question? Thank you for your help

Hi Roland2rule,
Let's take a look at your question.

$$\left(x+2\right)^2=-4+10x$$
Evaluate Left hand side,
$$x^2+4x+4=-4+10x$$
$$x^2+4x+4+4-10x=0$$
$$x^2+4x-10x+4+4=0$$
$$x^2-6x+8=0$$

Let's now factorize it by grouping method,
$$x^2-4x-2x+8=0$$
$$x\left(x-4\right)-2\left(x-4\right)=0$$
$$\left(x-2\right)\left(x-4\right)=0$$
$$\left(x-2\right)=0,\ \left(x-4\right)=0$$
$$x=2,\ 4$$

Therefore, by factorizing, we got two values of x i.e. 2 and 4.

But in the given options we can only find 2, therefore Option A is correct.

Hope it helps.
I am available if you'd like any followup.

GMAT Prep From The Economist
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by Scott@TargetTestPrep » Mon Nov 11, 2019 1:22 pm

BTGmoderatorRO wrote:If (x + 2)^2 = âˆ’ 4 + 10x , then which of the following could be the value of x?

A) 2
B) 1
C) 0
D) âˆ’1
E) âˆ’2
OA is a
Can anyone help me with the solution to this question? Thank you for your help