Find the two numbers using a quadratic equation

One number is equal to the square of another.  Find the numbers if both are positive and their sum is 2450. 
​

x = one number 
2450 - x = other number   {the sum of the two numbers is 2450}

2450 - x = x²    {one number equals square of another}
x² + x - 2450 = 0    {subtracted 2450 from each side and added x}
(x + 50)(x - 49) = 0    {factored into two binomials}
x + 50 = 0  or  x - 49 = 0    {set equal to zero}
x = -50   or   x = 49    {solved each equation for x}

Only using the positive number, 49.

2450 - x = 2401    {substituted 49, in for x, into (2450 - x)}

49 and 2401 are the two numbers 

​Ask Algebra House