If x^2 + 3x + 3 = 5x + 6 then x equals

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Oct 03, 2018 10:06 pm

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If x^2 + 3x + 3 = 5x + 6 then x equals

a. -1 or 3
b. -1 or 4
c. 0 or 3
d. 0 or 6
e. 1 or 3

OA A

Source: EMPOWERgmat

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Source: Beat The GMAT — Problem Solving | Wed Oct 03, 2018 10:06 pm

nonplus2: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Mon May 07, 2018 8:47 am; Location: India; GMAT Score:610

by nonplus2 » Thu Oct 04, 2018 5:37 am

x^2 + 3x + 3 = 5x + 6 ==> x^2 - 2x -3 = 0
=> x^2 - 3x + x - 3 = 0 ==> x*(x - 3) + 1*(x - 3) = 0
=> (x - 3)(x + 1) = 0
=> x = 3 or x = -1

Correct answer is A

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Oct 04, 2018 7:17 am

BTGmoderatorDC wrote:If xÂ² + 3x + 3 = 5x + 6 then x equals

a. -1 or 3
b. -1 or 4
c. 0 or 3
d. 0 or 6
e. 1 or 3

nonplus2's approach is the as mine, but a reasonably fast alternative approach is to test the answer choices .

Answer choice A suggests that one possible solution is x = -1
So, plug x = -1 into the equation to get: (-1)Â² + 3(-1) + 3 = 5(-1) + 6
Simplify to get: 1 = 1. Perfect!!!
So, x = -1 IS a solution.
We can ELIMINATE C, D and E, because they don't include x = -1 as a solution.

We're down to just A and B, so let's test another value x-value. Let's test x = 3
Plug it in to get: (3)Â² + 3(3) + 3 = 5(3) + 6
Simplify to get: 21 = 21. Perfect!!!
So, x = 3 IS a solution.
ELIMINATE B

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sat Oct 06, 2018 1:23 am

Collect like terms.
$$x^2\ +\ 3x\ -\ 5x\ =\ 6\ -\ 3$$
$$x^2\ -2x\ =\ 3$$
$$x^2\ -2x\ -\ 3\ =\ 0$$
= Quadratic equation factorizing.
(x - 3) (x + 1) = 0
x - 3 = 0 or x + 1 = 0
x = 3 or x = -1

Option A is CORRECT.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Oct 07, 2018 6:29 pm

BTGmoderatorDC wrote:If x^2 + 3x + 3 = 5x + 6 then x equals

a. -1 or 3
b. -1 or 4
c. 0 or 3
d. 0 or 6
e. 1 or 3

Simplifying, we have:

x^2 - 2x - 3 = 0

(x - 3)(x + 1) = 0

x = 3 or x = -1

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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