SOLUTION: The product of two consecutive numbers is 72. Find the smaller of the numbers

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Question 188302: The product of two consecutive numbers is 72. Find the smaller of the numbers
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want the numbers to be positive.


"The product of two consecutive numbers is 72" translates to x%28x%2B1%29=72


x%28x%2B1%29=72 Start with the given equation.


x%5E2%2Bx=72 Distribute


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


x+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-72%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--288+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-72%29 to get -288


x+=+%28-1+%2B-+sqrt%28+1%2B288+%29%29%2F%282%281%29%29 Rewrite sqrt%281--288%29 as sqrt%281%2B288%29


x+=+%28-1+%2B-+sqrt%28+289+%29%29%2F%282%281%29%29 Add 1 to 288 to get 289


x+=+%28-1+%2B-+sqrt%28+289+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-1+%2B-+17%29%2F%282%29 Take the square root of 289 to get 17.


x+=+%28-1+%2B+17%29%2F%282%29 or x+=+%28-1+-+17%29%2F%282%29 Break up the expression.


x+=+%2816%29%2F%282%29 or x+=++%28-18%29%2F%282%29 Combine like terms.


x+=+8 or x+=+-9 Simplify.


So the answers are x+=+8 or x+=+-9


However, we only want the positive numbers. So the only answer is x=8


This means that the smaller number is 8.