%5E2-25%3D0.jpeg "(x+6)^2-25=0")
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.