2-81%3D0.jpeg "(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.