(x-6)%3D20.jpeg "(x-5)(x-6)=20")
Solving the Quadratic Equation: (x-5)(x-6) = 20
This article will guide you through the steps of solving the quadratic equation (x-5)(x-6) = 20.
1. Expanding the Equation
First, we need to expand the left side of the equation by using the distributive property (or FOIL method):
(x-5)(x-6) = x² - 6x - 5x + 30
Simplifying, we get:
x² - 11x + 30 = 20
2. Setting the Equation to Zero
To solve for x, we need to bring all terms to one side of the equation, making the other side equal to zero:
x² - 11x + 30 - 20 = 0
This simplifies to:
x² - 11x + 10 = 0
3. Factoring the Quadratic Equation
Now, we need to factor the quadratic equation:
(x - 1)(x - 10) = 0
4. Solving for x
Finally, we set each factor equal to zero and solve for x:
- x - 1 = 0 => x = 1
- x - 10 = 0 => x = 10
Therefore, the solutions to the equation (x-5)(x-6) = 20 are x = 1 and x = 10.
Conclusion
We successfully solved the quadratic equation (x-5)(x-6) = 20 by expanding the equation, setting it to zero, factoring it, and finally solving for x. This process demonstrates how to approach and solve quadratic equations using factoring.