# SOLUTION: The sum of two numbers is seven. The sum of the squares of the two numbers is twenty-nine. Find the two numbers.

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 Question 314054: The sum of two numbers is seven. The sum of the squares of the two numbers is twenty-nine. Find the two numbers. Answer by unlockmath(1602)   (Show Source): You can put this solution on YOUR website!Hello, Let x be one number and y the the other. We'll set up 2 equations as: x+y=7 x^2+y^2=29 Now do substitution: x=7-y Plug this into the second equation: (7-y)^2+y^2=29 Expand it out to: 49-14y+y^2+y^2=29 Subtract 29 from both sides to get: 2y^2-14y+20=0 Factor out a 2 to get: 2(y^2-7y+10)=0 Factor: 2(y-2)(y-5)=0 Solve for y to get: y=2 y=5 So we know x can be 2 and 5 Make sense? RJ www.math-unlock.com