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What is the value of x? (1) x^2 + 4x = –8x – 35 (2) x^2 + 3x = –7x – 2

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Bunuel
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What is the value of x? (1) x^2 + 4x = –8x – 35 (2) x^2 + 3x = –7x – 2 [#permalink] New post   26 Jul 2018, 00:09
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What is the value of x?

(1) x^2 + 4x = –8x – 35
(2) x^2 + 3x = –7x – 25
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Re: What is the value of x? (1) x^2 + 4x = –8x – 35 (2) x^2 + 3x = –7x – 2 [#permalink] New post   26 Jul 2018, 00:22
Bunuel wrote:
What is the value of x?

(1) x^2 + 4x = –8x – 35
(2) x^2 + 3x = –7x – 25


OA: B
Statement 1 :\(x^2 + 4x = –8x – 35\)
\(x^2 + 12x+35=0\)
\(x^2 + 7x+5x+7*5=0\)
\((x+7)(x+5)=0\)
\(x=-5,-7\)
Two different value of \(x\) , hence Statement 1 alone is not sufficient.

Statement 2:\(x^2 + 3x = –7x – 25\)
\(x^2 + 10x+25 =0\)
\(x^2 + 5x+5x+5*5 =0\)
\((x+5)(x+5)=0\)
\(x=-5\)
1 unique value of \(x\) , hence Statement 2 alone is sufficient.
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What is the value of x? (1) x^2 + 4x = –8x – 35 (2) x^2 + 3x = –7x – 2 [#permalink] New post   26 Jul 2018, 00:23
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What is the value of x?

A quadratic equation has almost always two roots. if the equation is in the form of \(a^2-2ab+b^2\) or \(a^2+2ab+b^2\), when both the roots are same, the value will be one...

(1) x^2 + 4x = –8x – 35
\(x^2+12x+35=0\)...Had this been \(x^2+12x+36=0\), we would have had only one value as \(x^2+12x+36=0........x^2+2*1*6x+6^2=0\)
but now there will be two values
insuff

(2) x^2 + 3x = –7x – 25
\(x^2+10x+25=0............x^2+2*1*5x+5^2=0..........(x+5)^2=0\)
hence x is -5
sufficient

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Re: What is the value of x? (1) x^2 + 4x = –8x – 35 (2) x^2 + 3x = –7x – 2 [#permalink] New post   03 Jan 2019, 20:27
I think the key to getting this problem right is:

What is the value of x? Dont think that previous comments stressed it enough

The here indicates that there is only 1 possible solution that we are looking for. Algebra in the previous comments is good and you can look at it to see how to arrive to just 1 value.

I think
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Re: What is the value of x? (1) x^2 + 4x = –8x – 35 (2) x^2 + 3x = –7x – 2 [#permalink]
03 Jan 2019, 20:27
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Bunuel
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