Question

(2x+1)^2-(2x+3)(2x-3)=0

Answer 1

Смотри.......................

Answer 2

To solve the equation $(2x+1)^2-(2x+3)(2x-3)=0$, we'll first expand and simplify the expression on the left side and then proceed with solving for $x$:

Step 1: Expand and simplify

$(2x+1)^2 = (2x+1)(2x+1) = 4x^2 + 4x + 1$

$(2x+3)(2x-3) = 2x(2x-3) + 3(2x-3) = 4x^2 - 6x + 6x - 9 = 4x^2 - 9$

Now, let's put it back into the original equation:

$4x^2 + 4x + 1 - (4x^2 - 9) = 0$

Step 2: Combine like terms

$4x^2 + 4x + 1 - 4x^2 + 9 = 0$

Step 3: Simplify further

$4x^2 - 4x^2 + 4x + 1 + 9 = 0$

$4x + 10 = 0$

Step 4: Isolate $x$

$4x = -10$

$x = \frac{-10}{4}$

Step 5: Simplify the fraction

$x = -\frac{5}{2}$

So, the solution to the equation is $x = -\frac{5}{2}$.