SOLUTION: one number is 10 less than five times number. their product is 120. find the numbers

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Question 761541: one number is 10 less than five times number. their product is 120. find the numbers
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
FIrst number is 10 less than 5 times second number.
Let second number be x
First number is then 5*x - 10
Product = x+%2A+%285%2Ax+-+10%29+=+120
5%2Ax%5E2+-+10%2Ax+-+120+=+0

x%5E2+-+2%2Ax+-+24+=+0
Solving for x, x = +6 or -4.
First number can be 20 or -30
Possible solutions are (20,6) and (-30,-4)
Solution for the above quadratic equation is shown through solver below.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-24+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-24=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%28-2%29-sqrt%28+100+%29%29%2F2%5C1+=+-4

Quadratic expression 1x%5E2%2B-2x%2B-24 can be factored:
1x%5E2%2B-2x%2B-24+=+1%28x-6%29%2A%28x--4%29
Again, the answer is: 6, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-24+%29