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Let (x,y) be an ordered pair of real numbers that satisfies the equation x^2 + y^2 = 14x + 40y. What is the minimum value of x?

 Apr 27, 2022
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Rewrite this equation as: \(x^2-14x+y^2-40y=0\)

 

Completing the square, we have: \((x-7)^2+(y-20)^2=449\)

 

The minimum value for x is the center (7) - the radius.

 

The radius is the square root of the number on the right-hand side. 

 

You should be able to take it from here!

 Apr 27, 2022

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