What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?

Question

What is the larger of the 2 solutions of the equation  x^2  − 4x = 96 ?
 A. 8
 B. 12
 C. 16
 D. 32
 E. 100

OG Q 2017(Book Question: 68)

diegocml · Accepted Answer

Simply set the quadratic equation to zero and factor the roots out.

{ x }^{ 2 }-4x=96\ { x }^{ 2 }-4x-96=0\ \left( x+8 ight) \left( x-12 ight) =0\ x=-8,\quad x=12

For those people, like me, who struggle to find the roots, I suggest using one approach I took from  pacifist85 .

Prime factorize the constant and see which number combinations that sum to 4 and multiply to 96.

96={ 2 }^{ 5 }\ast { 3 }^{ 1 }

You will eventually find the 8 and 12 roots.

sashiim20 · Answer

Solving Quadratic equation x^2 − 4x = 96 x^2 - 4x - 96 = 0 x^2 - 12x - 8x - 96 = 0 x (x - 12) + 8 (x - 12) = 0 (x + 8) (x - 12) x = 12, -8 x=12 is larger value Therefore Answer is B...... Please, consider giving kudos if you find my answer helpful in any way

10046844 · Answer

B. 12

(x-12) (x+8) so solutions are 12, -8

Abhishek009 · Answer

x^2  −  4x  =  96

Or,  x^2  −  4x  −  96  = 0

Or,  x^2   −12x  +  8x  −  96  = 0

Or, x ( x - 12 ) + 8 ( x - 12 ) = 0

Or x = 12 , -8
 
So , The larger of the 2 solutions must be (B) 12

Abhishek009 · Answer

x^2 − 4x = 96

Or,  x^2 − 4x − 96 = 0

Or,  x^2 − x ( 12 − 8 ) − 96 = 0

Or,  x^2 − 12x + 8x − 96 = 0

Or,  x ( x − 12 ) + 8( x − 12 ) = 0

So,  x = 12  ,  − 8

Thus, larger of the 2 numbers is 12 , answer must be (B) 12

mahdwen · Answer

x^2 - 4x - 96 = 0 
 x^2 - 4x + 4 - 100 = 0 
 (x-2)^2 = 100 
 x-2 = 10  or  x-2 = -10 
roots are 12 and -8, with 12 being the larger. => Answer B

danlew · Answer

The solution should be one of the roots of x^2−4x−96=0

Working from the answer choices, we can work backwards to see if we get an integer quotient by dividing 96 by the answer choice and then checking if we can get a -4 as the difference between the quotient and the answer choice.

Only B fits the scenarios as 96/12 = 8 and 12-8 is 4.

longhaul123 · Answer

I have a question here. So in the equation given : x^2 - 4x =96 then x(x-4)=96 therefore x=96 or x-4=96 x=100
I know for the fact that this method is incorrect. But am not understanding why is it incorrect. can someone please help me

anhht13 · Answer

x^2−4x=96 => (x-12)*(x+8) = 0. > x = 12 or x = -8 => answer B

ScottTargetTestPrep · Answer

Let’s solve the given quadratic:

x^2 - 4x - 96 = 0

(x + 8)(x - 12) = 0

x = -8 or x = 12

The larger of the two solutions is 12.

Answer: B

MonkeyWork21 · Answer

Solving for quadratic is definitely the fastest route to an answer on this one but one could also simply test answer choices in a relatively fast manner as well w/o actually having to do much math (either start from E given we are looking for the "larger" of two solutions or use the optimal B/D approach)

E) 100^2 - 4(100) = 96 --> clearly doesn't work (recognize here that the x^2 needs to be a lot smaller)
D) 32^2 - 4(32) = 96 --> same rationale as above (x^2 still too big)
C) 16^2 - 4(16) = 96 --> x^2 still too big but getting closer...
B) 12^2 - 4(12) = 96 --> looks promising so do a quick check...144 - 48 = 96 --> correct answer choice

Answer = B

Abhishek009 · Answer

x^2 − 4x - 96 = 0

Or,  x^2 − 12x +8x - 96 = 0

Or,  x(x - 12) +8( x - 12) = 0

Either x = -8 or x = 12, Thus Answer must be (B)

hasnain3047 · Answer

(x-12)(x+8)=0
x=12, x=-8
So larger solution is 12

Answer B

Posted from my mobile device

Salsanousi · Answer

It might take a few attempts to know the two factors that once multiplied result in 96

We can choose from the answer choices

16 and 12 have a difference of 4 but will definitely have a multiple larger than 96.

So it is between 12 and 8 then it must be 12.

Answer choice B

Kinshook · Answer

x^2-12x*8x-96=0
(x-12)(x+8)=0
x = 12 or -8
Larger solution = 12

IMO B

Posted from my mobile device

LeenaSai · Answer

Hi all ,

Why can’t we solve this question as:
X(x-4) = 96 
 X = 96 , x = 100 
 Larger one is 100

Kindly guide

Posted from my mobile device

goaltop30mba · Answer

Instead of evaluating 96 for appropriate roots, one can also solve this by just rearranging the equation

x^2 +4-4x-4=96

(x-2)^2=100

(x-2)^2 - (10)^2 = 0 — this is a^2 - b^2

Hence we can straightaway get the two roots ie 12 and -8

Posted from my mobile device

bumpbot · Answer

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What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?

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What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?

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