(x-4)%3D(x%2B2)%5E2.jpeg "(x+10)(x-4)=(x+2)^2")
Solving the Equation: (x+10)(x-4) = (x+2)^2
This equation presents a quadratic equation that can be solved using algebraic manipulation. Let's break down the steps:
1. Expand both sides of the equation
- Left side: (x+10)(x-4) = x² - 4x + 10x - 40 = x² + 6x - 40
- Right side: (x+2)² = (x+2)(x+2) = x² + 2x + 2x + 4 = x² + 4x + 4
Now, the equation becomes: x² + 6x - 40 = x² + 4x + 4
2. Simplify the equation
Subtract x² from both sides: 6x - 40 = 4x + 4 Subtract 4x from both sides: 2x - 40 = 4 Add 40 to both sides: 2x = 44
3. Solve for x
Divide both sides by 2: x = 22
Conclusion
Therefore, the solution to the equation (x+10)(x-4) = (x+2)² is x = 22.