If 4 is one solution of the equation x^2 + 3x + k = 10, wher

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BTGmoderatorAT: Moderator; Posts: 426; Joined: Tue Aug 22, 2017 8:48 pm; Followed by:1 members

If 4 is one solution of the equation x^2 + 3x + k = 10, wher

by BTGmoderatorAT » Sat Jan 27, 2018 6:28 am

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

I'm confused how to set up the formulas here. Can any experts help?

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Source: Beat The GMAT — Problem Solving | Sat Jan 27, 2018 6:28 am

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

by Brent@GMATPrepNow » Sat Jan 27, 2018 7:08 am

ardz24 wrote:If 4 is one solution of the equation xÂ² + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Let's first determine the value of k.

Since x = 4 is a solution to the equation xÂ² + 3x + k = 10, we know that x = 4 SATISFIES the equation.
That is: 4Â² + 3(4) + k = 10
Evaluate to get: 16 + 12 + k = 10
Solve for k to get: k = -18

So, the ORIGINAL equation is xÂ² + 3x + (-18) = 10
This is the same as: xÂ² + 3x - 18 = 10
We now need to solve this equation.

First, set it equal to zero: xÂ² + 3x - 28 = 0
Factor: (x + 7)(x - 4) = 0
So, x = -7 or x = 4

We already know that x = 4 is one solution.
So, the other solution is x = -7

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jul 28, 2019 8:40 am

BTGmoderatorAT wrote:If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

I'm confused how to set up the formulas here. Can any experts help?

Since x = 4, we have:

4^2 + (3)(4) + k = 10

16 + 12 + k = 10

28 + k = 10

k = -18

Next we plug -18 into the given equation for k and then solve for x.

x^2 + 3x - 18 = 10

x^2 + 3x - 28 = 0

(x + 7)(x - 4) = 0

x = -7 or x = 4

Thus, -7 is the other solution.

Answer A

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