%5E2%2B5%3D-11.jpeg "(x-3)^2+5=-11")
Solving the Equation: (x-3)^2 + 5 = -11
This equation presents a challenge because a squared term can never be negative. Let's break down why this is the case and how to approach it:
Understanding the Problem
- Squares are always non-negative: Any number, whether positive or negative, when squared results in a non-negative value. For example, (-5)^2 = 25 and 5^2 = 25.
- The equation is impossible: The left side of the equation, (x-3)^2 + 5, will always be greater than or equal to 5 (since the squared term is always non-negative). It can never equal -11.
Conclusion
The equation (x-3)^2 + 5 = -11 has no real solutions. There is no real number x that can satisfy this equation.
What to do next?
If you encountered this equation in a problem, it's important to recognize that it is impossible to solve. There might be an error in the problem itself, or it could be designed to test your understanding of square terms and their properties.