What is the center of the circle 2x^2 + 3x + 2y^2 - 5y + 26 = 0

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The equation of a circle in center-radius form is (x - a)^2 + (y - b)^2 = r^2 where the radius of the circle is (a, b) and the radius is r.

2x^2 + 3x + 2y^2 - 5y + 26 = 0

=> x^2 + 3x/2 + y^2 - 5y/2 + 13 = 0

=> x^2 + 3x/2 + 9/16 + y^2 - 5y/2 + 25/16 + 13 = 9/16 + 25/16

=> (x + 3/4)^2 + (y - 5/4)^2 = -13 + 34/16 = -87/8

It is seen that the value for the square of radius is negative in this case. This is not possible.

The equation 2x^2 + 3x + 2y^2 - 5y + 26 = 0 is not that of a real circle.

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