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(x-18)^2=1

2 min read Jun 17, 2024
(x-18)^2=1

Solving the Equation (x-18)^2 = 1

This equation represents a simple quadratic equation that can be solved using a couple of methods. Here's how to approach it:

1. Taking the Square Root of Both Sides

  • Step 1: Take the square root of both sides of the equation: √[(x-18)^2] = ±√1
  • Step 2: Simplify: x - 18 = ±1
  • Step 3: Isolate 'x' by adding 18 to both sides: x = 18 ± 1

This gives us two possible solutions:

  • x = 18 + 1 = 19
  • x = 18 - 1 = 17

2. Expanding and Solving the Quadratic

  • Step 1: Expand the left side of the equation: (x - 18)(x - 18) = 1 x^2 - 36x + 324 = 1
  • Step 2: Move all terms to one side: x^2 - 36x + 323 = 0
  • Step 3: Factor the quadratic equation: (x - 17)(x - 19) = 0
  • Step 4: Set each factor equal to zero and solve for 'x': x - 17 = 0 or x - 19 = 0 x = 17 or x = 19

Therefore, the solutions to the equation (x-18)^2 = 1 are x = 17 and x = 19.

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