(2x-5)2-81=0

2 min read Jun 16, 2024
(2x-5)2-81=0

Solving the Quadratic Equation: (2x - 5)² - 81 = 0

This article will guide you through solving the quadratic equation (2x - 5)² - 81 = 0. We will use the following steps:

1. Expanding the Equation

First, expand the square term:

(2x - 5)² = (2x - 5)(2x - 5) = 4x² - 20x + 25

Now, substitute this back into the original equation:

4x² - 20x + 25 - 81 = 0

Simplify the equation:

4x² - 20x - 56 = 0

2. Simplifying the Equation

We can simplify the equation by dividing both sides by 4:

x² - 5x - 14 = 0

3. Factoring the Equation

Now, we can factor the quadratic expression:

(x - 7)(x + 2) = 0

4. Solving for x

For the product of two factors to be zero, at least one of them must be zero. Therefore:

  • x - 7 = 0 => x = 7
  • x + 2 = 0 => x = -2

Conclusion

Therefore, the solutions to the quadratic equation (2x - 5)² - 81 = 0 are x = 7 and x = -2.

Related Post