(x%2B2)%2B3(x-4)(x%2B4)%3D2(2x%2B3)%5E2-8.jpeg "(5x-1)(x+2)+3(x-4)(x+4)=2(2x+3)^2-8")
Solving the Equation: (5x-1)(x+2)+3(x-4)(x+4)=2(2x+3)^2-8
This article will guide you through the steps of solving the equation: (5x-1)(x+2)+3(x-4)(x+4)=2(2x+3)^2-8
Expanding the Equation
First, we need to expand all the products in the equation:
- (5x-1)(x+2) = 5x² + 10x - x - 2 = 5x² + 9x - 2
- 3(x-4)(x+4) = 3(x² - 16) = 3x² - 48
- 2(2x+3)² = 2(4x² + 12x + 9) = 8x² + 24x + 18
Now the equation becomes:
5x² + 9x - 2 + 3x² - 48 = 8x² + 24x + 18 - 8
Simplifying the Equation
Next, we combine like terms on both sides of the equation:
8x² + 9x - 50 = 8x² + 24x + 10
Subtracting 8x² and 10 from both sides:
9x - 50 = 24x + 10
Subtracting 9x and 10 from both sides:
-60 = 15x
Solving for x
Finally, dividing both sides by 15 gives us the solution:
x = -4
Therefore, the solution to the equation (5x-1)(x+2)+3(x-4)(x+4)=2(2x+3)^2-8 is x = -4.