SOLUTION: the square of anumber exceeds 11 times the number by 312. find the number.

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Question 36848: the square of anumber exceeds 11 times the number by 312. find the number.
Found 2 solutions by checkley71, vidhyak:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
X~2=11X+312 OR X~2-11X-312=0 OR (X-24)(X+13)=0 OR X=24 & X=-13

Answer by vidhyak(98) About Me  (Show Source):
You can put this solution on YOUR website!
the square of anumber exceeds 11 times the number by 312. find the number.

Let the number be x and sqaure of the number x^2
x^2 - 11x = 312
x^2 - 11x - 312 = 0

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-11x%2B-312+=+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=%28-11%29%5E2-4%2A1%2A-312=1369.

Discriminant d=1369 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+1369+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+1369+%29%29%2F2%5C1+=+24
x%5B2%5D+=+%28-%28-11%29-sqrt%28+1369+%29%29%2F2%5C1+=+-13

Quadratic expression 1x%5E2%2B-11x%2B-312 can be factored:
1x%5E2%2B-11x%2B-312+=+1%28x-24%29%2A%28x--13%29
Again, the answer is: 24, -13. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-11%2Ax%2B-312+%29