(3x-1)2-5(x-2)-(2x+3)2-(5x+2)(x-1)=0

2 min read Jun 16, 2024

Solving the Quadratic Equation: (3x-1)² - 5(x-2) - (2x+3)² - (5x+2)(x-1) = 0

This article will guide you through the process of solving the quadratic equation (3x-1)² - 5(x-2) - (2x+3)² - (5x+2)(x-1) = 0. We will break down the steps to make it clear and easy to follow.

Step 1: Expanding the Equation

First, we need to expand the equation by using the distributive property and the FOIL method:

(3x-1)²: (3x-1)(3x-1) = 9x² - 6x + 1
-5(x-2): -5x + 10
(2x+3)²: (2x+3)(2x+3) = 4x² + 12x + 9
-(5x+2)(x-1): -5x² + 3x + 2

Now, we can substitute these expanded expressions back into the original equation:

9x² - 6x + 1 - 5x + 10 - 4x² - 12x - 9 - 5x² + 3x + 2 = 0

Step 2: Combining Like Terms

Next, we combine the like terms on the left side of the equation:

(9x² - 4x² - 5x²) + (-6x - 5x - 12x + 3x) + (1 + 10 - 9 + 2) = 0

This simplifies to:

0x² - 20x + 4 = 0

Step 3: Simplifying the Equation

We can further simplify the equation by dividing both sides by 4:

-5x + 1 = 0

Step 4: Solving for x

Finally, we solve for x by isolating it on one side of the equation:

-5x = -1

x = 1/5

Conclusion

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