SOLUTION: If the square of a positive number is increased by the number, the result is 12. What is the number ?

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Question 949587: If the square of a positive number is increased by the number, the result is 12. What is the number ?
Found 2 solutions by macston, ankor@dixie-net.com:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
If the square of a positive number is increased by the number, the result is 12. What is the number ?
n= the number
n%5E2%2Bn=12 Subtract 12 from each side.
n%5E2%2Bn-12=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation an%5E2%2Bbn%2Bc=0 (in our case 1n%5E2%2B1n%2B-12+=+0) has the following solutons:

n%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=%281%29%5E2-4%2A1%2A-12=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+49+%29%29%2F2%5Ca.

n%5B1%5D+=+%28-%281%29%2Bsqrt%28+49+%29%29%2F2%5C1+=+3
n%5B2%5D+=+%28-%281%29-sqrt%28+49+%29%29%2F2%5C1+=+-4

Quadratic expression 1n%5E2%2B1n%2B-12 can be factored:
1n%5E2%2B1n%2B-12+=+1%28n-3%29%2A%28n--4%29
Again, the answer is: 3, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-12+%29

ANSWER: Since we are looking for a positive number, the answer is 3
CHECK:
n%5E2%2Bn=12
3%5E2%2B3=12
9%2B3=12
12=12

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If the square of a positive number is increased by the number, the result is 12.
x^2 + x = 12
x^2 + x - 12 = 0
Factors to
(x+4)(x-3) = 0
What is the number ?
x = 3, the positive number