SOLUTION: The sum of a positive number and its square is 12. What is the number?

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Question 185547: The sum of a positive number and its square is 12. What is the number?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"The sum of a positive number and its square is 12" translates to x%2Bx%5E2=12


x%2Bx%5E2=12 Start with the given equation.


x%2Bx%5E2-12=0 Subtract 12 from both sides.


x%5E2%2Bx-12=0 Rearrange the terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=1, and c=-12


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%28-12%29+%29%29%2F%282%281%29%29 Plug in a=1, b=1, and c=-12


x+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--48+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-12%29 to get -48


x+=+%28-1+%2B-+sqrt%28+1%2B48+%29%29%2F%282%281%29%29 Rewrite sqrt%281--48%29 as sqrt%281%2B48%29


x+=+%28-1+%2B-+sqrt%28+49+%29%29%2F%282%281%29%29 Add 1 to 48 to get 49


x+=+%28-1+%2B-+sqrt%28+49+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-1+%2B-+7%29%2F%282%29 Take the square root of 49 to get 7.


x+=+%28-1+%2B+7%29%2F%282%29 or x+=+%28-1+-+7%29%2F%282%29 Break up the expression.


x+=+%286%29%2F%282%29 or x+=++%28-8%29%2F%282%29 Combine like terms.


x+=+3 or x+=+-4 Simplify.


So the possible answers are x+=+3 or x+=+-4



However, the problem states that the number is positive. So we must ignore x=-4


So the only answer is x=3 which means that the number is 3