(x-4)^2-25=0

less than a minute read Jun 17, 2024

Solving the Equation: (x-4)^2 - 25 = 0

This equation is a quadratic equation in disguise. Let's break down how to solve it:

We can rewrite the equation by recognizing that 25 is the square of 5:

(x-4)^2 - 5^2 = 0

Now, we can apply the difference of squares factorization:

(a^2 - b^2) = (a+b)(a-b)

Applying this to our equation:

(x-4+5)(x-4-5) = 0

This simplifies to:

(x+1)(x-9) = 0

For the product of two factors to be zero, at least one of the factors must be zero. Therefore, we have two possible solutions:

The solutions to the equation (x-4)^2 - 25 = 0 are x = -1 and x = 9.