(x%2B7)-(x%2B5)(x-1)%3D0.jpeg "(x-3)(x+7)-(x+5)(x-1)=0")
Solving the Equation: (x-3)(x+7)-(x+5)(x-1)=0
This article will guide you through the process of solving the equation (x-3)(x+7)-(x+5)(x-1)=0. We will use algebraic manipulation and simplification to find the solution(s) for x.
Expanding the Equation
First, we need to expand the equation by multiplying the terms within the parentheses. Using the FOIL method (First, Outer, Inner, Last) for each set of parentheses, we get:
- (x-3)(x+7) = x² + 7x - 3x - 21 = x² + 4x - 21
- (x+5)(x-1) = x² - x + 5x - 5 = x² + 4x - 5
Substituting these back into the original equation, we have:
(x² + 4x - 21) - (x² + 4x - 5) = 0
Simplifying the Equation
Next, we simplify the equation by combining like terms:
x² + 4x - 21 - x² - 4x + 5 = 0 -16 = 0
Analyzing the Result
We arrive at the equation -16 = 0. This is a contradiction, as -16 can never be equal to 0.
Therefore, the equation (x-3)(x+7)-(x+5)(x-1)=0 has no solution.
Conclusion
The equation (x-3)(x+7)-(x+5)(x-1)=0 has no solution. This is because the simplified form of the equation leads to a contradiction.