(X+3)2+y2=64

Solution for (X+3)2+y2=64 equation:

(X+3)2+X2=64

We move all terms to the left:

(X+3)2+X2-(64)=0

We add all the numbers together, and all the variables

X^2+(X+3)2-64=0

We multiply parentheses

X^2+2X+6-64=0

We add all the numbers together, and all the variables

X^2+2X-58=0

a = 1; b = 2; c = -58;
Δ = b2-4ac
Δ = 22-4·1·(-58)
Δ = 236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{59}}{2*1}=\frac{-2-2\sqrt{59}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{59}}{2*1}=\frac{-2+2\sqrt{59}}{2}
$