%5E2%3D16.jpeg "(x-7)^2=16")
Solving the Equation (x - 7)² = 16
This equation involves a squared term, which means we need to use the square root property to solve it. Here's how to break it down:
Understanding the Equation
The equation (x - 7)² = 16 states that the square of the expression (x - 7) equals 16. To find the value of x, we need to isolate it.
Solving for x
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Take the square root of both sides: √[(x - 7)²] = ±√16
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Simplify: x - 7 = ±4
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Isolate x: x = 7 ± 4
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Calculate the two possible solutions:
- x = 7 + 4 = 11
- x = 7 - 4 = 3
The Solutions
Therefore, the solutions to the equation (x - 7)² = 16 are x = 11 and x = 3.
Verification
You can always verify your solutions by substituting them back into the original equation:
- For x = 11: (11 - 7)² = 4² = 16 (True)
- For x = 3: (3 - 7)² = (-4)² = 16 (True)
Both solutions satisfy the original equation, confirming their validity.