SOLUTION: When a number is subtracted from its square, the difference 90. Find the number(s).

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Question 944597: When a number is subtracted from its square, the difference 90. Find the number(s).
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number
x%5E2-x=90
x%5E2-x-90=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-90+=+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=%28-1%29%5E2-4%2A1%2A-90=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+361+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+361+%29%29%2F2%5C1+=+10
x%5B2%5D+=+%28-%28-1%29-sqrt%28+361+%29%29%2F2%5C1+=+-9

Quadratic expression 1x%5E2%2B-1x%2B-90 can be factored:
1x%5E2%2B-1x%2B-90+=+1%28x-10%29%2A%28x--9%29
Again, the answer is: 10, -9. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-90+%29

The answers are 10 and -9
CHECK
for 10
10%5E2-10=90
100-10=90
90=90
for -9
-9%5E2-%28-9%29=90
81-%28-9%29=90
90=90
So both answers check. The answers are 10 and -9.