SOLUTION: I've wracked my brain trying to translate this word problem into the proper quadratic equation so that I can solve it. I know what the numbers are but can't figure out the proper

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Question 5153: I've wracked my brain trying to translate this word problem into the proper quadratic equation so that I can solve it. I know what the numbers are but can't figure out the proper format. Here's the problem -
"The sum of two numbers is 10. The sum of the squares of the two numbers is 58. Write and solve an equation to find the two numbers."
Thanks!!!
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Let first number be x. Since both add to 10, the other number must be 10-x.

other info.... x%5E2+%2B+%2810-x%29%5E2+=+58
x%5E2+%2B+100+-+20x+%2B+x%5E2+=+58
2x%5E2+-+20x+%2B+100+=+58
2x%5E2+-+20x+%2B+42+=+0
x%5E2+-+10x+%2B+21+=+0
(x-7)(x-3) = 0
so x-7=0 or x-3=0

so x is 3 or 7...the 2 are interchangeable results ie the 2 numbers are 3 and 7.

jon.