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Which of the following could be a solution of the equation
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30 Nov 2021, 06:45
30 Nov 2021, 06:45
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Which of the following could be a solution of the equation \(x^2 − 7x − 18 = 0 ?\)
(A) −1
(B) 0
(C) 2
(D) 7
(E) 9
(A) −1
(B) 0
(C) 2
(D) 7
(E) 9
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Which of the following could be a solution of the equation
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30 Nov 2021, 07:14
30 Nov 2021, 07:14
1
Carcass wrote:
Which of the following could be a solution of the equation \(x^2 − 7x − 18 = 0 ?\)
(A) −1
(B) 0
(C) 2
(D) 7
(E) 9
(A) −1
(B) 0
(C) 2
(D) 7
(E) 9
Approach #2: Algebra
Take: \(x^2 − 7x − 18 = 0\)
Factor the left side: \((x - 9)(x + 2) = 0\)
So, EITHER \(x = 9\) OR \(x = -2\)
Answer: E
Approach #2: Test each answer choice
(A) −1.
Plug this possible x-value into the equation to get: \((-1)^2 − 7(-1) − 18 = 0\)
Simplify: 1 + 7 - 18 = 0. Doesn't work. Eliminate.
(B) 0
Here, we get: \(0^2 − 7(0) − 18 = 0\)
Simplify: 0 - 0 - 18 = 0. Doesn't work. Eliminate.
(C) 2
Here, we get: \(2^2 − 7(2) − 18 = 0\)
Simplify: 4 - 14 - 18 = 0. Doesn't work. Eliminate.
(D) 7
Here, we get: \(7^2 − 7(7) − 18 = 0\)
Simplify: 49 - 49 - 18 = 0. Doesn't work. Eliminate.
(E) 9
Here, we get: \(9^2 − 7(9) − 18 = 0\)
Simplify: 81 - 63 - 18 = 0. WORKS!
Answer: E
General Discussion
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: Which of the following could be a solution of the equation
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10 Dec 2023, 20:03
10 Dec 2023, 20:03
1
\(x^2 − 7x − 18 = 0\)
=> We need to split the middle term to get two terms whose sum is equal to the middle term and product is equal to the product of first term and last term
=> \(x^2 − 9x + 2x − 18 = 0\)
As, -9x + 2x = -7x And -9x * 2x = \(x^2\) * -18 = -18\(x^2\)
=> x * ( x-9) + 2*(x - 9) = 0
=> (x - 9) * (x + 2) = 0
=> x = 9 or -2
So, Answer will be E
Hope it helps!
=> We need to split the middle term to get two terms whose sum is equal to the middle term and product is equal to the product of first term and last term
=> \(x^2 − 9x + 2x − 18 = 0\)
As, -9x + 2x = -7x And -9x * 2x = \(x^2\) * -18 = -18\(x^2\)
=> x * ( x-9) + 2*(x - 9) = 0
=> (x - 9) * (x + 2) = 0
=> x = 9 or -2
So, Answer will be E
Hope it helps!
