(x-7)^2=0

Jasonbradley

2 min read

·

Jun 17, 2024

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Solving the Equation (x-7)^2 = 0

This equation represents a simple quadratic equation. Let's break down how to solve it:

Understanding the Equation

The equation (x-7)^2 = 0 is a squared term set equal to zero. This means that the expression inside the parentheses must be equal to zero.

Solving for x

1. Take the square root of both sides:
   √(x-7)^2 = √0
2. Simplify: x - 7 = 0
3. Isolate x: x = 7

Solution

Therefore, the only solution to the equation (x-7)^2 = 0 is x = 7.

Graphical Representation

The equation (x-7)^2 = 0 represents a parabola that touches the x-axis at the point (7, 0). This means the equation has a single, repeated root at x = 7.

Key Takeaways

• When a squared term is equal to zero, the expression inside the square must be zero.
• Solving this type of equation involves taking the square root and isolating the variable.
• The solution represents the point where the graph of the equation intersects the x-axis.