(x-5)(x-6)=2

2 min read Jun 17, 2024

Solving the Quadratic Equation: (x-5)(x-6) = 2

This article will guide you through solving the quadratic equation (x-5)(x-6) = 2. We will explore the steps involved in finding the solutions for x.

Expanding the Equation

First, we need to expand the left side of the equation by multiplying the binomials:

(x-5)(x-6) = 2

x² - 11x + 30 = 2

Rearranging the Equation

To solve for x, we need to set the equation to zero:

x² - 11x + 28 = 0

Factoring the Equation

Now, we factor the quadratic expression:

(x-4)(x-7) = 0

Finding the Solutions

For the product of two factors to be zero, at least one of the factors must be zero. Therefore, we have two possible solutions:

x - 4 = 0 => x = 4
x - 7 = 0 => x = 7

Conclusion

The solutions to the quadratic equation (x-5)(x-6) = 2 are x = 4 and x = 7. These values, when substituted into the original equation, will make the equation true.