%5E2%3D0.jpeg "(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
- Take the square root of both sides: √((x-6)^2) = √0
- Simplify: This simplifies to (x-6) = 0
- Solve for x: Add 6 to both sides of the equation: x - 6 + 6 = 0 + 6
- 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.