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(x+7)(x-1)=(x+1)^2

less than a minute read Jun 17, 2024
(x+7)(x-1)=(x+1)^2

Solving the Equation: (x+7)(x-1) = (x+1)^2

This equation involves expanding and simplifying both sides to solve for x. Let's break down the steps:

1. Expanding the Equation

  • Left side: (x+7)(x-1) = x² - x + 7x - 7 = x² + 6x - 7

  • Right side: (x+1)² = (x+1)(x+1) = x² + x + x + 1 = x² + 2x + 1

2. Simplifying the Equation

Now we have: x² + 6x - 7 = x² + 2x + 1

3. Solving for x

  • Subtract x² from both sides: 6x - 7 = 2x + 1
  • Subtract 2x from both sides: 4x - 7 = 1
  • Add 7 to both sides: 4x = 8
  • Divide both sides by 4: x = 2

Conclusion

Therefore, the solution to the equation (x+7)(x-1) = (x+1)² is x = 2.

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