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Math Expert V
Joined: 02 Sep 2009
Posts: 58431
Which of the following is a solution to the equation 4x^2−7x−49=5x+63?  [#permalink]

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

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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

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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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4x^2-12x-112=0
x^2-3x-28=0
(x-7)(x+4)=0
x = 7 or x = -4
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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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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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GMAT Club Legend  V
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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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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!

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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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1
1
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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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

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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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