%5E2-(2x-3)(2x%2B3)%3D0.jpeg "(2x-5)^2-(2x-3)(2x+3)=0")
Solving the Equation: (2x-5)^2 - (2x-3)(2x+3) = 0
This equation involves simplifying expressions and solving a quadratic equation. Let's break down the steps:
1. Expand the expressions
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(2x-5)^2: This is a perfect square trinomial. We can expand it using the formula (a-b)^2 = a^2 - 2ab + b^2. (2x-5)^2 = (2x)^2 - 2(2x)(5) + 5^2 = 4x^2 - 20x + 25
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(2x-3)(2x+3): This is a difference of squares, which can be expanded using the formula (a-b)(a+b) = a^2 - b^2. (2x-3)(2x+3) = (2x)^2 - 3^2 = 4x^2 - 9
2. Substitute the expanded expressions into the original equation
Now our equation becomes: 4x^2 - 20x + 25 - (4x^2 - 9) = 0
3. Simplify the equation
Combine like terms: 4x^2 - 20x + 25 - 4x^2 + 9 = 0 -20x + 34 = 0
4. Solve for x
Isolate x: -20x = -34 x = -34 / -20 x = 17/10
Conclusion
Therefore, the solution to the equation (2x-5)^2 - (2x-3)(2x+3) = 0 is x = 17/10.