(5x-1)(x+1)-2(x-3)^2=(x+2)(3x-1)-(x+4)^2+(x^2-x)

2 min read Jun 16, 2024
(5x-1)(x+1)-2(x-3)^2=(x+2)(3x-1)-(x+4)^2+(x^2-x)

Solving the Equation: (5x-1)(x+1)-2(x-3)^2=(x+2)(3x-1)-(x+4)^2+(x^2-x)

This article will guide you through the process of solving the given equation:

(5x-1)(x+1)-2(x-3)^2=(x+2)(3x-1)-(x+4)^2+(x^2-x)

Step 1: Expanding the Equation

Start by expanding all the products and squares in the equation:

  • (5x-1)(x+1) = 5x² + 4x - 1
  • -2(x-3)² = -2(x² - 6x + 9) = -2x² + 12x - 18
  • (x+2)(3x-1) = 3x² + 5x - 2
  • -(x+4)² = -(x² + 8x + 16) = -x² - 8x - 16

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

5x² + 4x - 1 - 2x² + 12x - 18 = 3x² + 5x - 2 - x² - 8x - 16 + x² - x

Step 2: Combining Like Terms

Next, combine the terms on both sides of the equation:

3x² + 16x - 19 = 3x² - 4x - 26

Step 3: Isolating the Variable

To solve for x, bring all the x terms to one side and the constant terms to the other:

16x + 4x = -26 + 19

20x = -7

Step 4: Solving for x

Finally, divide both sides by 20 to isolate x:

x = -7/20

Conclusion

Therefore, the solution to the equation (5x-1)(x+1)-2(x-3)²=(x+2)(3x-1)-(x+4)²+(x²-x) is x = -7/20.

Related Post


Featured Posts