(x-5)(x-6)=25/24^2

3 min read Jun 17, 2024

Solving the Equation: (x-5)(x-6) = 25/24^2

This equation presents a quadratic equation that we can solve to find the values of x. Here's a step-by-step breakdown of the solution process:

1. Expand the Left Side

Start by expanding the left side of the equation using the distributive property (also known as FOIL):

(x-5)(x-6) = x^2 - 6x - 5x + 30

Simplifying:

x^2 - 11x + 30 = 25/24^2

2. Move the Constant Term to the Left Side

To get the equation in standard quadratic form (ax^2 + bx + c = 0), move the constant term from the right side to the left side:

x^2 - 11x + 30 - 25/24^2 = 0

3. Calculate and Simplify the Constant Term

Calculate the value of 25/24^2 and subtract it from 30:

x^2 - 11x + 30 - (25/576) = 0

x^2 - 11x + (17280 - 25)/576 = 0

x^2 - 11x + 17255/576 = 0

4. Solve the Quadratic Equation

Now you have a quadratic equation in standard form. You can solve for x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where:

a = 1
b = -11
c = 17255/576

Substitute the values into the quadratic formula and simplify to find the two solutions for x.

5. The Solution(s)

After solving the quadratic formula, you will find the two possible values for x. These solutions represent the points where the graph of the equation intersects the x-axis.

Important Note: The quadratic formula will likely result in two distinct solutions. If you find only one solution, it means that the solution is a double root.

By following these steps, you can successfully solve the equation (x-5)(x-6) = 25/24^2 and find the values of x that satisfy the equation.