Expanding the left side:
(2x-5)^2 = (2x-5)(2x-5) = 4x^2 - 10x - 10x + 25= 4x^2 - 20x + 25
Substituting this back into the equation:
4x^2 - 20x + 25 - 0.5x = (2x-1)(2x+1) - 154x^2 - 20.5x + 25 = 4x^2 - 1 - 154x^2 - 20.5x + 25 = 4x^2 - 16-20.5x + 25 = -16-20.5x = -41x = 2
Therefore, the solution to the given equation is x=2.
Expanding the left side:
(2x-5)^2 = (2x-5)(2x-5) = 4x^2 - 10x - 10x + 25
= 4x^2 - 20x + 25
Substituting this back into the equation:
4x^2 - 20x + 25 - 0.5x = (2x-1)(2x+1) - 15
4x^2 - 20.5x + 25 = 4x^2 - 1 - 15
4x^2 - 20.5x + 25 = 4x^2 - 16
-20.5x + 25 = -16
-20.5x = -41
x = 2
Therefore, the solution to the given equation is x=2.