(5x-9)(x-1)-x(x-2)=0

2 min read Jun 16, 2024
(5x-9)(x-1)-x(x-2)=0

Solving the Equation: (5x-9)(x-1)-x(x-2)=0

This article will guide you through the process of solving the given quadratic equation: (5x-9)(x-1)-x(x-2)=0.

Step 1: Expand the Equation

First, we need to expand the equation by multiplying out the brackets:

  • (5x-9)(x-1) = 5x² - 5x - 9x + 9 = 5x² - 14x + 9
  • x(x-2) = x² - 2x

Now our equation looks like this: 5x² - 14x + 9 - (x² - 2x) = 0

Step 2: Simplify the Equation

Next, we simplify the equation by combining like terms:

  • 5x² - x² - 14x + 2x + 9 = 0
  • 4x² - 12x + 9 = 0

Step 3: Solve for x

We can now solve for x using the quadratic formula. The quadratic formula is:

x = (-b ± √(b² - 4ac)) / 2a

Where:

  • a = 4
  • b = -12
  • c = 9

Substituting these values into the quadratic formula, we get:

x = (12 ± √((-12)² - 4 * 4 * 9)) / (2 * 4)

x = (12 ± √(144 - 144)) / 8

x = (12 ± √0) / 8

x = 12 / 8

x = 3/2

Therefore, the solution to the equation (5x-9)(x-1)-x(x-2)=0 is x = 3/2.

Conclusion

By following the steps outlined above, we successfully solved the quadratic equation. Remember, the quadratic formula is a powerful tool for solving equations of this type. Always ensure you simplify and expand the equation correctly to avoid errors.

Related Post


Featured Posts