What is (x^2+5x+25/4)+y^2= 25/4+25/4 ?

The solution to (x^2+5x+25/4)+y^2= 25/4+25/4 is Circle with (a,b)=(-5/2 ,0),r= 5/(sqrt(2))

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(x^2+5x+25/4)+y^2= 25/4+25/4

(x^{2} + 5 x + \frac{25}{4}) + y^{2} = \frac{25}{4} + \frac{25}{4}

(a, b) = (- \frac{5}{2}, 0), r = \frac{5}{2}

Solution steps

x^{2} + 5 x + \frac{25}{4} + y^{2} = \frac{25}{4} + \frac{25}{4}

Rewrite

x^{2} + 5 x + \frac{25}{4} + y^{2} = \frac{25}{4} + \frac{25}{4}

in the form of the standard circle equation

(x - (- \frac{5}{2}))^{2} + (y - 0)^{2} = (\frac{5}{2})^{2}

Therefore the circle properties are:

(a, b) = (- \frac{5}{2}, 0), r = \frac{5}{2}

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What is (x^2+5x+25/4)+y^2= 25/4+25/4 ?
The solution to (x^2+5x+25/4)+y^2= 25/4+25/4 is Circle with (a,b)=(-5/2 ,0),r= 5/(sqrt(2))