%5E2-(x-5)%5E2-2x%2B1%3D0.jpeg "(x+5)^2-(x-5)^2-2x+1=0")
Solving the Equation (x+5)^2 - (x-5)^2 - 2x + 1 = 0
This article will guide you through solving the equation (x+5)^2 - (x-5)^2 - 2x + 1 = 0. We will use algebraic manipulation to simplify the equation and find the solution for x.
1. Expanding the Squares
Start by expanding the squares using the formula (a+b)^2 = a^2 + 2ab + b^2 and (a-b)^2 = a^2 - 2ab + b^2.
(x+5)^2 = x^2 + 10x + 25 (x-5)^2 = x^2 - 10x + 25
Now, substitute these expanded terms back into the original equation:
(x^2 + 10x + 25) - (x^2 - 10x + 25) - 2x + 1 = 0
2. Simplifying the Equation
Next, simplify the equation by removing parentheses and combining like terms:
x^2 + 10x + 25 - x^2 + 10x - 25 - 2x + 1 = 0
This simplifies to:
18x + 1 = 0
3. Solving for x
Finally, solve for x by isolating it on one side of the equation:
18x = -1 x = -1/18
Therefore, the solution to the equation (x+5)^2 - (x-5)^2 - 2x + 1 = 0 is x = -1/18.
Conclusion
By expanding the squares, simplifying the equation, and isolating x, we successfully solved the equation (x+5)^2 - (x-5)^2 - 2x + 1 = 0, finding that x = -1/18.