(x+6)^2-25=0

Jasonbradley

2 min read Jun 17, 2024

Solving the Equation (x+6)^2 - 25 = 0

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

1. Simplify the Equation

We can simplify the equation by using the difference of squares factorization:

(a² - b²) = (a + b)(a - b)

Applying this to our equation, we get:

(x + 6)² - 25 = 0
[(x + 6) + 5][(x + 6) - 5] = 0
(x + 11)(x + 1) = 0

2. Solve for x

Now we have a simple product of two factors equaling zero. This means at least one of the factors must be zero. So we have two possible solutions:

x + 11 = 0
x + 1 = 0

Solving for x in each case:

x = -11
x = -1

3. Solution

Therefore, the solutions to the equation (x + 6)² - 25 = 0 are x = -11 and x = -1.

Conclusion

By simplifying the equation and using the difference of squares factorization, we were able to solve the quadratic equation (x + 6)² - 25 = 0 and find its two solutions.