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Bunuel
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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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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Bunuel
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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