(x-2)%2B(x-7)(x%2B7)%3D(3x%2B1)%5E2-(3x-2)(3x%2B2).jpeg "(-x+5)(x-2)+(x-7)(x+7)=(3x+1)^2-(3x-2)(3x+2)")
Solving the Equation: (-x+5)(x-2)+(x-7)(x+7)=(3x+1)^2-(3x-2)(3x+2)
This article will guide you through the process of solving the given equation:
(-x+5)(x-2)+(x-7)(x+7)=(3x+1)^2-(3x-2)(3x+2)
Step 1: Expand the Products
- Left-hand side:
- (-x+5)(x-2) = -x² + 7x - 10
- (x-7)(x+7) = x² - 49
- Right-hand side:
- (3x+1)² = 9x² + 6x + 1
- (3x-2)(3x+2) = 9x² - 4
Step 2: Combine Like Terms
- Left-hand side: -x² + 7x - 10 + x² - 49 = 7x - 59
- Right-hand side: 9x² + 6x + 1 - 9x² + 4 = 6x + 5
Step 3: Simplify the Equation
The equation now becomes: 7x - 59 = 6x + 5
Step 4: Solve for x
- Subtract 6x from both sides: x - 59 = 5
- Add 59 to both sides: x = 64
Therefore, the solution to the equation (-x+5)(x-2)+(x-7)(x+7)=(3x+1)^2-(3x-2)(3x+2) is x = 64.
Important Note: Remember to always check your solution by substituting it back into the original equation to ensure it holds true.