SOLUTION: I am having difficulty solving the following problem. Can someone please assist me in doing so. Thanks! One number is 6 less than another. The product of the number is 72. Find th

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Question 169972: I am having difficulty solving the following problem. Can someone please assist me in doing so. Thanks!
One number is 6 less than another. The product of the number is 72. Find the numbers.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"One number is 6 less than another." translates to y=x-6


"The product of the number is 72" translates to x%2Ay=72


x%2Ay=72 Start with the second equation


x%28x-6%29=72 Plug in y=x-6


x%5E2-6x=72 Distribute.


x%5E2-6x-72=0 Subtract 72 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-6, and c=-72


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%28-72%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-6, and c=-72


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%28-72%29+%29%29%2F%282%281%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%281%29%28-72%29+%29%29%2F%282%281%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36--288+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-72%29 to get -288


x+=+%286+%2B-+sqrt%28+36%2B288+%29%29%2F%282%281%29%29 Rewrite sqrt%2836--288%29 as sqrt%2836%2B288%29


x+=+%286+%2B-+sqrt%28+324+%29%29%2F%282%281%29%29 Add 36 to 288 to get 324


x+=+%286+%2B-+sqrt%28+324+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%286+%2B-+18%29%2F%282%29 Take the square root of 324 to get 18.


x+=+%286+%2B+18%29%2F%282%29 or x+=+%286+-+18%29%2F%282%29 Break up the expression.


x+=+%2824%29%2F%282%29 or x+=++%28-12%29%2F%282%29 Combine like terms.


x+=+12 or x+=+-6 Simplify.


So the answers are x+=+12 or x+=+-6


This means that the numbers are:


12 and 6

OR...

-6 and -12