(x+2)(x-3)=(x-3)^2

2 min read Jun 16, 2024

Solving the Equation (x + 2)(x - 3) = (x - 3)^2

This equation involves a quadratic expression and presents a unique opportunity to practice algebraic manipulation and solving for unknown variables. Let's break down the steps to find the solution(s) for x.

Step 1: Expand both sides of the equation

First, we need to expand both sides of the equation to simplify the expression:

Left side: (x + 2)(x - 3) = x² - x - 6
Right side: (x - 3)² = (x - 3)(x - 3) = x² - 6x + 9

Now our equation becomes: x² - x - 6 = x² - 6x + 9

Step 2: Simplify the equation

We can simplify the equation by subtracting x² from both sides:

-x - 6 = -6x + 9

Step 3: Isolate the x term

Next, let's isolate the x term by adding 6x to both sides:

5x - 6 = 9

Step 4: Solve for x

Finally, we can solve for x by adding 6 to both sides and then dividing by 5:

5x = 15 x = 3

Conclusion

Therefore, the solution to the equation (x + 2)(x - 3) = (x - 3)² is x = 3.

It's important to note that this solution represents a single value where the equation holds true. This kind of equation often leads to a single solution, but there are cases where you might have multiple solutions or no solutions at all.