2-(x-5)2%3D9-solve-this.jpeg "(x+4)2-(x-5)2=9 Solve This")
Solving the Equation: (x+4)² - (x-5)² = 9
This equation involves simplifying and solving for the variable 'x'. Here's a step-by-step solution:
1. Expanding the Squares
We begin by expanding the squares using the formula: (a+b)² = a² + 2ab + b² and (a-b)² = a² - 2ab + b²
Applying this to our equation:
- (x + 4)² = x² + 8x + 16
- (x - 5)² = x² - 10x + 25
Now our equation becomes: x² + 8x + 16 - (x² - 10x + 25) = 9
2. Simplifying the Equation
Let's distribute the negative sign and combine like terms:
x² + 8x + 16 - x² + 10x - 25 = 9 18x - 9 = 9
3. Solving for x
Now we have a simple linear equation. Let's isolate 'x':
18x = 9 + 9 18x = 18 x = 18/18 x = 1
Conclusion
Therefore, the solution to the equation (x+4)² - (x-5)² = 9 is x = 1.