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

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

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

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

Step 1: Expand Both Sides

First, we need to expand both sides of the equation to get rid of the parentheses.

  • Left Side: Using the "difference of squares" pattern, (x-1)(x+1) simplifies to x² - 1.
  • Right Side: Distributing the 2, we get 2x² - 6.

Now, our equation looks like this: x² - 1 = 2x² - 6

Step 2: Rearrange the Equation

Next, let's rearrange the equation so all terms are on one side and set it equal to zero. Subtract x² from both sides and add 6 to both sides:

  • x² - 1 - x² + 6 = 2x² - 6 - x² + 6

This simplifies to: 5 = x²

Step 3: Solve for x

Finally, we need to solve for x. Take the square root of both sides:

  • √5 = √(x²)

Remember that taking the square root can result in both positive and negative solutions. Therefore:

  • x = ±√5

Conclusion

The solutions to the equation (x-1)(x+1) = 2(x²-3) are x = √5 and x = -√5.

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