%5E2%3D49.jpeg "(x-5)^2=49")
Solving the Equation (x - 5)² = 49
This equation involves a squared term, which means we'll need to use the square root property to solve for x. Here's a step-by-step solution:
1. Isolate the Squared Term
The squared term is already isolated on the left side of the equation.
2. Take the Square Root of Both Sides
Remember that taking the square root of a number results in both a positive and a negative solution.
√(x - 5)² = ±√49
3. Simplify
Simplify both sides of the equation:
x - 5 = ±7
4. Solve for x
Now we have two separate equations to solve:
- Equation 1: x - 5 = 7
- Equation 2: x - 5 = -7
Solving Equation 1:
x - 5 = 7
x = 7 + 5
x = 12
Solving Equation 2:
x - 5 = -7
x = -7 + 5
x = -2
Solution
Therefore, the solutions to the equation (x - 5)² = 49 are x = 12 and x = -2.