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Solving the Equation (x-2)^2 = 28
This article will guide you through the steps of solving the equation (x-2)^2 = 28.
Understanding the Equation
The equation (x-2)^2 = 28 is a quadratic equation in disguise. Let's break it down:
- (x-2)^2 represents the square of the expression (x-2). This means we are multiplying (x-2) by itself.
- 28 is the constant term on the right-hand side of the equation.
Solving for x
To solve for x, we need to isolate it. Here's how:
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Take the square root of both sides:
√[(x-2)^2] = ±√28
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Simplify:
x - 2 = ±√28
Note: Remember that taking the square root of a number results in both a positive and a negative solution.
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Simplify the radical:
x - 2 = ±2√7
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Isolate x:
x = 2 ± 2√7
The Solutions
Therefore, the solutions to the equation (x-2)^2 = 28 are:
- x = 2 + 2√7
- x = 2 - 2√7
Conclusion
By applying the steps of taking the square root and simplifying, we successfully solved the equation (x-2)^2 = 28. The solutions are x = 2 + 2√7 and x = 2 - 2√7.