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(x-1)^2-(x-3)(x+3)=4

2 min read Jun 17, 2024
(x-1)^2-(x-3)(x+3)=4

Solving the Equation: (x-1)^2 - (x-3)(x+3) = 4

This article will guide you through the process of solving the equation (x-1)^2 - (x-3)(x+3) = 4.

Understanding the Equation

The equation involves:

  • Squaring a binomial: (x-1)^2 represents the product of (x-1) multiplied by itself.
  • Difference of Squares: (x-3)(x+3) is a special product known as the difference of squares, which simplifies to x^2 - 9.

Solving the Equation

  1. Expand the squares: (x-1)^2 = x^2 - 2x + 1 (x-3)(x+3) = x^2 - 9

  2. Substitute the expanded terms back into the equation: x^2 - 2x + 1 - (x^2 - 9) = 4

  3. Simplify the equation: x^2 - 2x + 1 - x^2 + 9 = 4 -2x + 10 = 4

  4. Isolate the 'x' term: -2x = 4 - 10 -2x = -6

  5. Solve for 'x': x = -6 / -2 x = 3

Solution

Therefore, the solution to the equation (x-1)^2 - (x-3)(x+3) = 4 is x = 3.

Verification

We can verify our solution by substituting x = 3 back into the original equation:

(3-1)^2 - (3-3)(3+3) = 4 2^2 - 0 * 6 = 4 4 = 4

The equation holds true, confirming our solution is correct.

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