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Sub 505 (Easy)|   Algebra|      
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Bunuel
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If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ? 02 Sep 2025, 22:00
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If \(3x^2 + 2x + 9 = 2x^2 + 9x + 3\), what all the possible values of x ?

A. -6 and -1
B. -6 and 1
C. -1 and 6
D. 1 and 6
E. it cannot be determined from the information given.


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D
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If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ? 03 Sep 2025, 04:57
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First pull everything to the LHS and subtract like terms,
=> 3x^2 - 2x^2 + 2x - 9x + 9 - 3 = 0
=> x^2 - 7x + 6 = 0
=> (x-6)(x-1) = 0
=> x = 6 and 1

IMO D
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If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ? 03 Sep 2025, 05:46
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Bunuel
If \(3x^2 + 2x + 9 = 2x^2 + 9x + 3\), what all the possible values of x ?

A. -6 and -1
B. -6 and 1
C. -1 and 6
D. 1 and 6
E. it cannot be determined from the information given.


­
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Rearrange the equation we get ,

\(3x^2 + 2x + 9 - 2x^2 - 9x - 3 = 0 \)

\( x^2 - 7x + 6 = 0 \)

\( x^2 - 6x -x + 6 = 0 \)

x(x-6) -1(x-6) =0

(x-1)(x-6)=0

Thus, the values of x = 1 and 6.

Option D
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If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ? 03 Sep 2025, 07:08
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1st step in these type of questions is to think "How can I make this complex equation simple", and the easiest way is to move all elements to one side.

Moving all the elements to left, we have \(x^2\)-7x+6=0
This can be written as \(x^2\)-6x-x+6
Which can further be simplified into x(x-6)-1(x-6)---> (x-1)(x-6)
The roots are 1 and 6

Now, an alternate option is to plug answers and check, start with 1, 13=13 Good to go, now with -1, 10=-4(Not possible)
With 6 and 1, you will see the equation matching LHS and RHS.
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If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ? 03 Sep 2025, 18:18
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re arranging the eq we get :
x^2-7x+6=0
x^2-6x-x+6
x(x-6)-1(x-6)=0
(x-6)(x-1)=0
x=6,1. )option D
Bunuel
If \(3x^2 + 2x + 9 = 2x^2 + 9x + 3\), what all the possible values of x ?

A. -6 and -1
B. -6 and 1
C. -1 and 6
D. 1 and 6
E. it cannot be determined from the information given.


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If 3x^2 + 2x + 9 = 2x^2 + 9x + 3, what all the possible values of x ? 04 Sep 2025, 04:10
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We bring all terms to one side to convert the equation into the standard quadratic form \(ax^2 + bx + c = 0\)
\(3x^2 + 2x + 9 - (2x^2 + 9x + 3) = 0\)

We simplify by combining like terms
\(x^2 - 7x + 6 = 0\)

We factor the quadratic expression into binomials
\((x - 1)(x - 6) = 0\)

Answer The possible values of x are 1 and 6.

Hope this helps!
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