%5E2%3D25.jpeg "(x-9)^2=25")
Solving the Equation (x-9)^2 = 25
This equation involves a squared term, which means we need to use the square root property to solve it. Let's break down the steps:
Step 1: Take the Square Root of Both Sides
To get rid of the square, we take the square root of both sides of the equation:
√((x-9)²) = ±√25
This gives us:
x - 9 = ±5
Step 2: Solve for x
Now we have two separate equations to solve:
- Equation 1: x - 9 = 5
- Equation 2: x - 9 = -5
Solving Equation 1:
Add 9 to both sides: x = 5 + 9 x = 14
Solving Equation 2:
Add 9 to both sides: x = -5 + 9 x = 4
Step 3: The Solution
Therefore, the solutions to the equation (x-9)² = 25 are x = 14 and x = 4.
Important Note: Remember that when taking the square root of a number, there are always two possible solutions: a positive and a negative one. That's why we have the "±" sign in our equation.