%5E2%3D0.jpeg "(x-5)^2=0")
Solving the Equation: (x-5)^2 = 0
This equation represents a simple quadratic equation, but it's easy to solve using a few key steps.
Understanding the Equation
- (x-5)^2: This means we are squaring the expression (x-5).
- = 0: We are looking for the values of x that make this expression equal to zero.
Solving the Equation
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Take the square root of both sides: Since the left side is squared, we can get rid of the square by taking the square root of both sides. This gives us: √(x-5)^2 = √0
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Simplify: The square root of a squared expression is simply the original expression: x - 5 = 0
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Isolate x: To get x by itself, add 5 to both sides of the equation: x = 5
Solution
Therefore, the solution to the equation (x-5)^2 = 0 is x = 5.
What Does This Mean?
This solution tells us that the only value of x that satisfies the equation is 5. In other words, when x is equal to 5, the expression (x-5)^2 becomes zero.
Visual Representation
We can visualize this by thinking about the graph of the function y = (x-5)^2. This graph is a parabola that intersects the x-axis at the point x = 5. The fact that the equation (x-5)^2 = 0 has only one solution (x = 5) tells us that the parabola touches the x-axis at only this one point.