SOLUTION: sum of the squares of two numbers is 100. sum of the numbers is 2. find the numbers.

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Question 862390: sum of the squares of two numbers is 100. sum of the numbers is 2. find the numbers.
Answer by ben720(159) About Me  (Show Source):
You can put this solution on YOUR website!
Let first number = x
Let second = 2-x, as they add to two
x%5E2%2B%282-x%29%5E2=100
Square 2-x
x%5E2%2Bx%5E2-4x%2B4=100
Combine like terms
2x%5E2-4x%2B4=100
Divide both sides by 2
x%5E2-2x%2B2=50
Subtract 50 from both sides
x%5E2-2x-48=0
Use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%282+%2B-+sqrt%28+-2%5E2-4%2A1%2A-48+%29%29%2F%282%2A1%29+
x+=+%282+%2B-+sqrt%284%2B192%29%29%2F2+
x+=+%282+%2B-+sqrt%28196%29%29%2F2
x=%282%2B14%29%2F2ORx=%282-14%29%2F2
x=8ORx=-6

The numbers are 8 and -6