(x-9)^2=9

2 min read Jun 17, 2024

Solving the Equation (x-9)^2 = 9

This equation involves a squared term, which means we'll need to use the square root property to solve for x. Here's a step-by-step breakdown:

1. Take the Square Root of Both Sides

√[(x-9)^2] = ±√9

2. Simplify

x - 9 = ±3

3. Isolate x

x = 9 ± 3

4. Solve for the Two Possible Solutions

Solution 1: x = 9 + 3 = 12
Solution 2: x = 9 - 3 = 6

Therefore, the solutions to the equation (x-9)^2 = 9 are x = 12 and x = 6.

Understanding the Solutions

This equation represents a quadratic equation. The solutions we found, x = 12 and x = 6, are the x-intercepts of the parabola represented by the equation.

Let's visualize this:

Step 1: Expand the equation: (x-9)^2 = 9 becomes x^2 - 18x + 81 = 9
Step 2: Subtract 9 from both sides: x^2 - 18x + 72 = 0
Step 3: Factor the quadratic equation: (x - 12)(x - 6) = 0
Step 4: The roots of the equation are x = 12 and x = 6. These are the points where the parabola intersects the x-axis.

In conclusion, by applying the square root property, we successfully solved the equation (x-9)^2 = 9, finding two distinct solutions. We also explored the graphical interpretation of these solutions as the x-intercepts of the parabola represented by the equation.