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(x-8)^2-(x-4)(x+4)=0

less than a minute read Jun 17, 2024
(x-8)^2-(x-4)(x+4)=0

Solving the Equation: (x - 8)² - (x - 4)(x + 4) = 0

This equation involves expanding squares and products of binomials, and then simplifying to find the solution for x. Let's break down the steps:

1. Expand the Squares and Products

  • (x - 8)²: This is a perfect square trinomial. We can expand it as (x - 8)(x - 8) = x² - 16x + 64.
  • (x - 4)(x + 4): This is the difference of squares pattern. We can expand it as x² - 16.

Now, our equation becomes: x² - 16x + 64 - (x² - 16) = 0

2. Simplify the Equation

  • Distribute the negative sign: x² - 16x + 64 - x² + 16 = 0
  • Combine like terms: -16x + 80 = 0

3. Solve for x

  • Subtract 80 from both sides: -16x = -80
  • Divide both sides by -16: x = 5

Solution

Therefore, the solution to the equation (x - 8)² - (x - 4)(x + 4) = 0 is x = 5.

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