Mathematics

To find the center of a sphere, you need to rewrite the equation in standard form $(x-h)^2+(y-k)^2+(z-l)^2=r^2$ by completing the square for each variable. The key insight is that the linear terms $4x$, $-6y$, and $2z$ tell you exactly what to add and subtract—match each pair of terms to a perfect square, and the constants inside those squares reveal the center coordinates directly.

To find the center of a sphere, you need to rewrite the equation in standard form $(x-h)^2+(y-k)^2+(z-l)^2=r^2$ by completing the square for each variable. The key insight is that the linear terms $4x$, $-6y$, and $2z$ tell you exactly what to add and subtract—match each pair of terms to a perfect square, and the constants inside those squares reveal the center coordinates directly.