%5E2%3D25.jpeg "(x-4)^2=25")
Solving the Equation (x-4)^2 = 25
This equation involves a squared term and presents a simple example of solving quadratic equations. Let's break down the steps to find the solution(s) for x.
1. Isolate the Squared Term
First, we need to get the squared term (x-4)^2 by itself on one side of the equation. In this case, it already is!
2. Take the Square Root of Both Sides
To eliminate the square, we take the square root of both sides of the equation:
√[(x-4)^2] = ±√25
This gives us:
x - 4 = ±5
3. Solve for x
Now we have two separate equations to solve:
- Case 1: x - 4 = 5
- Case 2: x - 4 = -5
Solving for x in both cases:
- Case 1: x = 5 + 4 = 9
- Case 2: x = -5 + 4 = -1
Solution
Therefore, the solutions to the equation (x-4)^2 = 25 are x = 9 and x = -1.
Conclusion
By following these steps, we successfully solved the quadratic equation and found its two distinct solutions. Remember that when taking the square root of both sides, we need to consider both the positive and negative roots to ensure we capture all possible solutions.