ShmoopTube

00:02

Hope you left room for an extra helping of Shmoop.

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If 3x squared + 5x = 12 and x is not an integer, then what must x be?

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All right, so this question looks simple enough.

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We have to find the solution to this equation where x ISN’T an integer.

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So, first we can move 12 to the left side to get 3x squared + 5x – 12 = 0.

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This format look familiar to ya?

00:28

Well, it really doesn’t look like we can factor this one, so let’s apply the quadratic formula.

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So with 3 as a, 5 as b and negative 12, guest starring as c…we can now apply our formula.

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Negative 5 plus or minus radical 25 plus negative 4 times 3 times negative 12…equals 144 all over 6.

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…and 144 plus 25 is 169…ooh, magic number…

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…so we have negative 5 plus or minus 13…all over 6.

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Now we can just separate out the two plus or minus options…

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…and we have negative 5 plus 13 over 6 and negative 5 minus 13 over 6.

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The first one simplifies to 8 over 6, or just 4/3…

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…and the second one simplifies to negative 18 over 6, or just negative 3.

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So, since the question asks us for the non-integer solution to the equation,

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we can forget about that last one.

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Later, negative 3. So yeah…the answer is 4/3.

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