%5E2%3D18.jpeg "(x-2)^2=18")
Solving the Equation (x - 2)^2 = 18
This article will guide you through the steps to solve the equation (x - 2)^2 = 18.
Understanding the Equation
The equation represents a quadratic equation, meaning it involves a variable raised to the power of two. To solve for x, we need to isolate it.
Solving for x
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Take the square root of both sides: √(x - 2)^2 = ±√18
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Simplify: x - 2 = ±√(9 * 2) x - 2 = ±3√2
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Isolate x: x = 2 ± 3√2
Solutions
Therefore, the solutions to the equation (x - 2)^2 = 18 are:
- x = 2 + 3√2
- x = 2 - 3√2
Verification
You can verify these solutions by substituting them back into the original equation.
- For x = 2 + 3√2: ((2 + 3√2) - 2)^2 = (3√2)^2 = 18
- For x = 2 - 3√2: ((2 - 3√2) - 2)^2 = (-3√2)^2 = 18
Both solutions satisfy the original equation.
Conclusion
The equation (x - 2)^2 = 18 has two solutions: x = 2 + 3√2 and x = 2 - 3√2. These solutions can be found by isolating x through algebraic manipulation.