(x-3)^2-(x+5)^2=0

2 min read Jun 17, 2024

Solving the Equation (x-3)^2 - (x+5)^2 = 0

This equation involves the difference of squares, a pattern that we can use to simplify the equation and solve for x.

The difference of squares pattern states: a² - b² = (a + b)(a - b)

In our equation, a = (x-3) and b = (x+5).

Let's apply the difference of squares pattern to our equation:

[(x-3) + (x+5)][(x-3) - (x+5)] = 0

Simplifying the expressions inside the brackets:

(2x + 2)(-8) = 0

Now we have a simple equation with one variable. To find the solutions for x, we need to find the values that make the product equal to zero:

Therefore, the solution to the equation (x-3)² - (x+5)² = 0 is x = -1.

We can verify our solution by substituting x = -1 back into the original equation:

(-1 - 3)² - (-1 + 5)² = 0 (-4)² - (4)² = 0 16 - 16 = 0 0 = 0

This confirms that x = -1 is the correct solution.