(2x+5)2-(2x-5)2 Solution

2 min read Jun 16, 2024
(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.

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