SOLUTION: Hi, can you please help me with this problem?? I am SO CONFUSED, please help!! We have Finals coming up and i don't have a clue how to do these word problems! Here is the problem:

Question 23426: Hi, can you please help me with this problem?? I am SO CONFUSED, please help!! We have Finals coming up and i don't have a clue how to do these word problems! Here is the problem: The sum of two numbers is 25 and the sum of their squares is 313. Find the numbers. (Hint: Let one of the numbers be x. Express the other number in terms of x.)
Help will be greatly appreciated! Thank you ever so much!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let one of the numbers be "x".
Then, the 2nd number is 25-x.
EQUATION:
The sum of the squares of the numbers is 313
x^2 + (25-x)^2= 313
x^2 + 625 -50x+x^2 = 313
2x^2-50x+312=0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 13, 12. Here's your graph:

x=1 (1st number)
25-x=13 (2nd number)
Cheers,
Stan H.
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