SUMMARY
The equation of the sphere given is 16x² + 16y² + 16z² - 96x + 32y = 5. By completing the square, the center of the sphere is determined to be (3, -1, 0). The radius calculation initially attempted was incorrect; the correct method involves ensuring that all terms added to the left side are multiplied by 16, leading to a radius of √15 / 4. This highlights the importance of maintaining balance in equations when manipulating algebraic expressions.
PREREQUISITES
- Understanding of completing the square in algebra
- Familiarity with the standard equation of a sphere
- Basic knowledge of algebraic manipulation
- Ability to solve quadratic equations
NEXT STEPS
- Review the standard form of a sphere's equation
- Practice completing the square with different equations
- Learn about the geometric interpretation of spheres in three-dimensional space
- Explore methods for solving algebraic equations involving multiple variables
USEFUL FOR
Students studying algebra, particularly those tackling geometry and three-dimensional shapes, as well as educators looking for examples of completing the square in practical applications.