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Which of the following is a solution to the equation 4x^2−7x−49=5x+63?

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Which of the following is a solution to the equation 4x^2−7x−49=5x+63?  [#permalink]

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New post 16 Feb 2017, 03:37
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

87% (01:46) correct 13% (02:11) wrong based on 161 sessions

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Re: Which of the following is a solution to the equation 4x^2−7x−49=5x+63?  [#permalink]

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New post 16 Feb 2017, 03:55
4x^2-12x-112=0
x^2-3x-28=0
(x-7)(x+4)=0
x = 7 or x = -4
answer is E
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Re: Which of the following is a solution to the equation 4x^2−7x−49=5x+63?  [#permalink]

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New post 16 Feb 2017, 09:04
Bunuel wrote:
Which of the following is a solution to the equation 4x^2−7x−49=5x+63?

A. 3
B. 4
C. 5
D. 6
E. 7


\(4x^2 −7x − 49 = 5x + 63\)

Or, \(4x^2 −12x − 112 = 0\)

Or, \(x^2 −3x − 28= 0\)

Or, \(x^2 −7x + 4x − 28= 0\)

Or, \(x( x −7) + 4(x − 7)= 0\)

Or, \((x + 4) ( x −7) = 0\)

So, \(x = -4\) or \(x = 7\)

So, Answer must be (E) 7
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Re: Which of the following is a solution to the equation 4x^2−7x−49=5x+63?  [#permalink]

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New post 16 Feb 2017, 10:40
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Bunuel wrote:
Which of the following is a solution to the equation 4x² − 7x − 49 = 5x + 63?

A. 3
B. 4
C. 5
D. 6
E. 7


The 2 posts above both show the algebraic solution, which is the fastest way to solve this question.
However, if you didn't consider the algebraic, you can still solve the questions by plugging in the answer choices.

A. 3
Replace x with 3 to get: 4(3²) − 7(3) − 49 = 5(3) + 63
Simplify: 36 - 21 - 49 = 15 + 63
I won't go any further, because I can see that the left side will evaluate to be NEGATIVE, and the right side will be POSITIVE

B. 4
Replace x with 4 to get: 4(4²) − 7(4) − 49 = 5(4) + 63
Simplify: 64 - 28 - 49 = 20 + 63
I won't go any further, because I can see that the left side will evaluate to be NEGATIVE, and the right side will be POSITIVE

.
.
.
E. 7
Replace x with 7 to get: 4(7²) − 7(7) − 49 = 5(7) + 63
Simplify: 196 - 49 - 49 = 35 + 63
Evaluate: 98 = 98
PERFECT!

Answer: E
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Re: Which of the following is a solution to the equation 4x^2−7x−49=5x+63?  [#permalink]

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New post 16 Jul 2017, 12:00
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Which of the following is a solution to the equation 4x^2−7x−49=5x+63?

\(4x^2 −7x − 49 = 5x + 63\)

\(4x^2 −12x − 112 = 0\)

\(x^2 −3x − 28= 0\)

\(x^2 −7x + 4x − 28= 0\)

\(x( x −7) + 4(x − 7)= 0\)

\((x + 4) ( x −7) = 0\)

\(x = -4\) OR

\(x = 7\)

As we do not have option -4 in the answer choice, the answer is straight \(x = 7\)

Hence, Answer is E

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Re: Which of the following is a solution to the equation 4x^2−7x−49=5x+63?  [#permalink]

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New post 20 Jul 2017, 16:40
Bunuel wrote:
Which of the following is a solution to the equation 4x^2−7x−49=5x+63?

A. 3
B. 4
C. 5
D. 6
E. 7


We can simplify the given equation:

4x^2 − 7x − 49 = 5x + 63

4x^2 − 12x − 112 = 0

x^2 − 3x − 28 = 0

(x − 7)(x + 4) = 0

x = 7 or x = -4

Answer: E
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Re: Which of the following is a solution to the equation 4x^2−7x−49=5x+63?  [#permalink]

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Re: Which of the following is a solution to the equation 4x^2−7x−49=5x+63?   [#permalink] 03 Nov 2018, 08:19
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