SOLUTION: what multiplies to get 5 and adds up to -7

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Question 720061: what multiplies to get 5 and adds up to -7
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Please include the full directions. I assume that the problem is "What two numbers multiplies to get and and adds up to -7" or something to that effect. (I'm guessing that it is two numbers because if there were more numbers we wouldn't be able to solve it and if it was one number it would be impossible.)

Let x = one number and y = the other number. From what we we've been given:
xy = 5
x + 5 = -7

We'll use the substitution method to solve. Solving the second equation for x we get:
x = -y - 7
Substituting this expression for x into the first equation we get:
(-y - 7)y = 5
Simplifying:
-y%5E2-7y=5
This is quadratic so we want one side to be zero. Since it's a little easier if the squared term has a positive coefficient, I'm going to subtract the entire left side from both sides:
0+=+y%5E2%2B7y%2B5
This doesn't factor so we resort to the quadratic formula:
y+=+%28-%287%29+%2B-+sqrt%28%287%29%5E2-4%281%29%285%29%29%29%2F2%281%29
Simplifying...
y+=+%28-%287%29+%2B-+sqrt%2849-4%281%29%285%29%29%29%2F2%281%29
y+=+%28-%287%29+%2B-+sqrt%2849-35%29%29%2F2%281%29
y+=+%28-%287%29+%2B-+sqrt%2814%29%29%2F2%281%29
y+=+%28-7+%2B-+sqrt%2814%29%29%2F2
which is short for:
y+=+%28-7+%2B+sqrt%2814%29%29%2F2 or y+=+%28-7+-+sqrt%2814%29%29%2F2
or
y+=+%28-7%29%2F2+%2B+sqrt%2814%29%2F2 or y+=+%28-7%29%2F2+-+sqrt%2814%29%2F2

These answers are so odd I'm suspect that you left out more than just the word "two" from the description of the problem. If you need to solve for x, too, then use these y values and the equation x = -y - 7 to find the x's.