ShmoopTube

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For a good time, solve this shmoopy question... Solve for y: 2y squared plus 7y plus 3 equals 0

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And here are the potential answers...

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Ok. It's just a basic factoring question. It's in the form of something squared plus something

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plus an integer equals zero.

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A bell should be going off when we see an equation like this.

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We just have to figure out what the factors are... and there's a bit of a curveball in

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here in that there's a 2 on the front end.

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So we know that one of the factors is going to be a 2, as in:

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The quantity 2y plus something times the quantity y plus something.

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Let's plug in some numbers to get the 3. It's kind of easy because 3 only has 2 factors:

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1 and 3...

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Now we have quantity 2y plus 1 times quantity y plus 3.

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If we multiply it out, we get 2y times y here, which is 2y squared.

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Then we have 2y times 3, which is 6y

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plus y times 1, which is just... y.

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6y plus y is 7y; then, 1 times 3 is just 3 so we're done.

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But now... how do we make the whole thing equal to zero? Well, one of the elements here

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has to BE zero.

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If y is negative 3 then this one is 3 minus 3 which is 0...

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...and here, it's just negative one half, because negative 1 half times 2 is negative

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1... and negative 1 plus positive 1 is zero.

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So the other answer is negative one half and the answer is A and C...

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...or option E.

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