2-(2x-5)2-solution.jpeg "(2x+5)2-(2x-5)2 Solution")
Solving the Equation (2x+5)² - (2x-5)²
This article aims to guide you through the solution of the equation (2x+5)² - (2x-5)². We will utilize algebraic manipulation to simplify the expression and ultimately find the value of x.
Step 1: Expanding the Squares
We start by expanding the squares using the formula (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b²:
(2x+5)² - (2x-5)² = (4x² + 20x + 25) - (4x² - 20x + 25)
Step 2: Simplifying the Expression
Now, we can simplify the expression by combining like terms:
4x² + 20x + 25 - 4x² + 20x - 25 = 40x
Step 3: Finding the Value of x
We are left with the simplified equation 40x = 0. To solve for x, we divide both sides by 40:
x = 0/40
Therefore, x = 0 is the solution to the equation (2x+5)² - (2x-5)² = 0.
Conclusion
By carefully applying algebraic rules, we were able to solve the equation (2x+5)² - (2x-5)² = 0. The solution, x = 0, is the only value of x that satisfies the equation.