%5E2-25%3D0.jpeg "(x+4)^2-25=0")
Solving the Equation: (x+4)^2 - 25 = 0
This equation is a quadratic equation in disguise. We can solve it using a few simple steps:
1. Simplify using the difference of squares pattern:
The expression on the left-hand side of the equation is in the form of a difference of squares: (a^2 - b^2), where a = x+4 and b = 5. We can factor this using the formula: (a + b)(a - b).
Applying this to our equation:
(x + 4 + 5)(x + 4 - 5) = 0
2. Simplify the expression:
(x + 9)(x - 1) = 0
3. Apply the Zero Product Property:
The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.
Therefore, either:
- x + 9 = 0 or
- x - 1 = 0
4. Solve for x:
- x + 9 = 0 --> x = -9
- x - 1 = 0 --> x = 1
Therefore, the solutions to the equation (x+4)^2 - 25 = 0 are x = -9 and x = 1.