(x-2)^2=18

2 min read Jun 17, 2024
(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

  1. Take the square root of both sides: √(x - 2)^2 = ±√18

  2. Simplify: x - 2 = ±√(9 * 2) x - 2 = ±3√2

  3. 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.

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