(x%2B5)%3D(x%2B2)(x%2B6).jpeg "(x+4)(x+5)=(x+2)(x+6)")
Solving the Equation: (x+4)(x+5) = (x+2)(x+6)
This equation involves expanding and simplifying expressions on both sides to find the value of 'x'. Let's break down the steps:
1. Expanding the Expressions
We begin by using the distributive property (FOIL method) to expand both sides of the equation:
- Left Side: (x+4)(x+5) = x² + 5x + 4x + 20 = x² + 9x + 20
- Right Side: (x+2)(x+6) = x² + 6x + 2x + 12 = x² + 8x + 12
Now, our equation looks like this: x² + 9x + 20 = x² + 8x + 12
2. Simplifying the Equation
Notice that we have x² on both sides. Subtracting x² from both sides will cancel it out:
(x² + 9x + 20) - x² = (x² + 8x + 12) - x²
This leaves us with: 9x + 20 = 8x + 12
3. Isolating 'x'
To isolate 'x', we need to move all the terms containing 'x' to one side and constants to the other side. Subtracting 8x from both sides:
(9x + 20) - 8x = (8x + 12) - 8x
This gives us: x + 20 = 12
Finally, subtracting 20 from both sides:
(x + 20) - 20 = 12 - 20
We get: x = -8
Conclusion
Therefore, the solution to the equation (x+4)(x+5) = (x+2)(x+6) is x = -8.