(x%2B1)-2(x-3)%5E2%3D(x%2B2)(3x-1)-(x%2B4)%5E2%2B(x%5E2-x).jpeg "(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.