(2x-7)^2-6(2x-7)(x-3)=0

2 min read Jun 16, 2024

Solving the Quadratic Equation: (2x-7)^2 - 6(2x-7)(x-3) = 0

This article will guide you through solving the quadratic equation (2x-7)^2 - 6(2x-7)(x-3) = 0. We'll use a combination of factoring and the quadratic formula to find the solutions.

Step 1: Factor out the common term

Notice that both terms in the equation have a common factor of (2x-7). Let's factor this out:

(2x-7)[(2x-7) - 6(x-3)] = 0

Step 2: Simplify the expression inside the brackets

Let's simplify the expression inside the brackets:

(2x-7)(2x-7 - 6x + 18) = 0

(2x-7)(-4x + 11) = 0

Step 3: Solve for x

Now we have a product of two factors equaling zero. This means at least one of the factors must be equal to zero. We can solve for x by setting each factor equal to zero:

Factor 1: 2x - 7 = 0
- 2x = 7
- x = 7/2
Factor 2: -4x + 11 = 0
- -4x = -11
- x = 11/4

Solution

Therefore, the solutions to the quadratic equation (2x-7)^2 - 6(2x-7)(x-3) = 0 are:

x = 7/2
x = 11/4