SOLUTION: The difference of twice a number and five is equal to the square of the difference of the number and fifteen. What is the number?

Algebra ->  Human-and-algebraic-language -> SOLUTION: The difference of twice a number and five is equal to the square of the difference of the number and fifteen. What is the number?      Log On


   

Question 85902: The difference of twice a number and five is equal to the square of the difference of the number and fifteen. What is the number?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
let x = the number
:
The difference of twice a number and five is equal to the square of the difference of the number and fifteen.
:
2x - 5 = (x-15)^2
:
What is the number?
2x - 5 = x^2 - 30x + 225; FOILed (x-15)*(x-15)
:
0 = x^2 - 30x - 2x + 225 + 5
:
x^2 - 32x + 230 = 0
:
I would think that a solution would be an integer, but it's not the case here.
:
Using the quadratic formula I got solutions of +10.90098 and 21.09902
:
Both of these values do satisfy the equation