(x-6)^2=0

2 min read Jun 17, 2024
(x-6)^2=0

Solving the Equation (x-6)^2 = 0

This equation represents a simple quadratic equation, which can be solved using a few basic steps.

Understanding the Equation

The equation (x-6)^2 = 0 states that the square of the expression (x-6) is equal to zero. The only way a square can be zero is if the expression itself is zero.

Solving for x

  1. Take the square root of both sides: √((x-6)^2) = √0
  2. Simplify: This simplifies to (x-6) = 0
  3. Solve for x: Add 6 to both sides of the equation: x - 6 + 6 = 0 + 6
  4. Result: This gives us the solution: x = 6

Interpretation

The solution x = 6 indicates that the equation is satisfied only when x has a value of 6. This can be further understood by substituting x = 6 back into the original equation:

(6 - 6)^2 = 0

(0)^2 = 0

0 = 0

This confirms that x = 6 is indeed the correct solution to the equation (x-6)^2 = 0.

Conclusion

Solving the equation (x-6)^2 = 0 involves understanding the concept of squares and applying basic algebraic operations. The solution, x = 6, highlights the importance of considering the factors that can result in a squared expression equaling zero.