SOLUTION: There are two factors of -36 such that one factor is 11 less than half of the other factor. Choose all the pairs of these factors. the choices are -2 and 18, -6 and 6, 3 and

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Question 748392: There are two factors of -36 such that one factor is 11 less than half of the other factor. Choose all the pairs of these factors.
the choices are
-2 and 18,
-6 and 6,
3 and -12,
4 and -9

Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
let two factors of -36 be x and y
if one factor is 11 less than half of the other factor, we have
x%2B11=y%2F2 => y=2x%2B22
and xy=-36
x%282x%2B22%29=-36
2x%5E2%2B22x%2B36=0
x%5E2%2B11x%2B18=0.....write 11x as 2x%2B9x
x%5E2%2B2x%2B9x%2B18=0
%28x%5E2%2B2x%29%2B%289x%2B18%29=0
x%28x%2B2%29%2B9%28x%2B2%29=0
%28x%2B9%29%28x%2B2%29=0
solutions:
x=-9
x=-2
then
y=2x%2B22 => y=2%28-9%29%2B22 => y=-18%2B22 => y=4
or
y=2x%2B22 => y=2%28-2%29%2B22 => y=-4%2B22 => y=18
so, pairs are:
x=-9 and y=4
or x=-2 and y=18

the choices are
-2 and 18,

we can check these choices too:
-6 and 6,....plug in y=2x%2B22
6=2%28-6%29%2B22
6=-12%2B22
6%3C%3E10......not a solution

3 and -12,....plug in y=2x%2B22
-12=2%2A3%2B22

-12%3C%3E28.....not a solution
4 and -9....plug in y=2x%2B22
-9=2%2A4%2B22
-9%3C%3E30.....not a solution

so, your solution is -2 and 18

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

There are two factors of -36 such that one factor is 11 less than half of the other factor. Choose all the pairs of these factors.
the choices are
-2 and 18,
-6 and 6,
3 and -12,
4 and -9

By observation, and a little arithmetic, it can be seen that the choices are: highlight_green%28-+2_and_18%29, and highlight_green%284_and+-+9%29

You can do the check!!

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