%5E2%3D16.jpeg "(x-9)^2=16")
Solving the Equation (x-9)^2 = 16
This equation is a quadratic equation in disguise. Here's how to solve it:
1. Take the square root of both sides
- √((x-9)²) = ±√16
- This simplifies to: x - 9 = ±4
2. Isolate x
- x = 9 ± 4
3. Find the two possible solutions
- x = 9 + 4 = 13
- x = 9 - 4 = 5
Therefore, the solutions to the equation (x-9)² = 16 are x = 13 and x = 5.
Explanation
The equation (x-9)² = 16 represents a situation where the square of the difference between 'x' and 9 is equal to 16. We use the square root property to undo the squaring operation and find the possible values of 'x'. Since the square root of 16 can be both positive and negative (4 and -4), we get two separate solutions.
Important Note: Remember that when taking the square root of both sides of an equation, we must consider both the positive and negative roots. This is because squaring a positive or negative number results in a positive number.