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:

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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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-50x%2B312+=+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=%28-50%29%5E2-4%2A2%2A312=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--50%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-50%29%2Bsqrt%28+4+%29%29%2F2%5C2+=+13
x%5B2%5D+=+%28-%28-50%29-sqrt%28+4+%29%29%2F2%5C2+=+12

Quadratic expression 2x%5E2%2B-50x%2B312 can be factored:
2x%5E2%2B-50x%2B312+=+2%28x-13%29%2A%28x-12%29
Again, the answer is: 13, 12. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-50%2Ax%2B312+%29

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