Question 234934
The answer is 600.

The equations used are:


x^2 = y - 24
(x+1)^2 = y + 25


You set:


y = x^2 + 24
y = (x+1)^2 - 25


Then you set:


x^2 + 24 = (x+1)^2 - 25


because they both equal y so they are equal to each other.


You solve for x.


The x^2 cancels out as shown below:


(x+1)^2 - x^2 = 49


This becomes:


x^2 + 2x + 1 - x^2 = 49


The x^2 cancels out so the equation becomes:


2x + 1 = 49


Subtract 49 from both sides to get:


2x - 48 = 0


The general form of a quadratic equation is:


ax^2 + bx + c


This means that:


a = 0
b = 2
c = -48


The discriminant is b^2 - 4ac


This becomes 2^2 - 4*0*-48 which becomes:


4


Unfortunately, since a = 0, the whole quadratic formula becomes:


-b +/- sqrt (b^2-4ac) / 2a


Since a = 0, this means the solution is undefined.


I'm not sure what they were trying to tell you here.


Your equation is a straight line, not a quadratic equation, because the x^2 term canceled out.


You have one solution and one solution only, but it is not a quadratic equation.





The answer becomes x = 24


24^2 = 576 + 24 = 600


25^2 = 625 - 25 = 600


The discriminant is described <a href = "http://www.regentsprep.org/Regents/math/algtrig/ATE3/discriminant.htm" target = "_blank">here !!!!!</a>