(x-2)(x-3)=2

Jasonbradley

less than a minute read

·

Jun 17, 2024

12

Share

Solving the Equation (x-2)(x-3) = 2

This equation represents a quadratic equation. Let's break down how to solve it:

Step 1: Expand the Equation

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

(x - 2)(x - 3) = 2

• x² - 5x + 6 = 2

Step 2: Move Constant to the Left Side

Next, subtract 2 from both sides to set the equation equal to zero:

• x² - 5x + 4 = 0

Step 3: Factor the Quadratic

Now, factor the quadratic expression:

• (x - 1)(x - 4) = 0

Step 4: Solve for x

Finally, set each factor equal to zero and solve for x:

• x - 1 = 0 => x = 1
• x - 4 = 0 => x = 4

Conclusion

Therefore, the solutions to the equation (x-2)(x-3) = 2 are x = 1 and x = 4.