%5E2%3D16.jpeg "(x-5)^2=16")
Solving the Equation (x - 5)^2 = 16
This equation involves a squared term, which we can solve by using the square root property. Here's how:
1. Isolate the Squared Term
The squared term is already isolated on the left side of the equation: (x - 5)^2 = 16
2. Take the Square Root of Both Sides
Taking the square root of both sides gives us: √((x - 5)^2) = ±√16
This results in: x - 5 = ±4
3. Solve for x
We now have two separate equations to solve:
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Equation 1: x - 5 = 4 Adding 5 to both sides, we get: x = 9
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Equation 2: x - 5 = -4 Adding 5 to both sides, we get: x = 1
Solution
Therefore, the solutions to the equation (x - 5)^2 = 16 are x = 9 and x = 1.
Checking the Solutions
We can verify our solutions by plugging them back into the original equation:
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For x = 9: (9 - 5)^2 = 4^2 = 16 (True)
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For x = 1: (1 - 5)^2 = (-4)^2 = 16 (True)
This confirms that both solutions are valid.