Question

Решить уравнение (2x+3)^2-(2x+5)(2x-5)=38

Answer 1

(2x+3)^2-(2x+5)(2x-5)=38

4x^2+12x+9-4x^2+25=38

12x=4

X=4/12=1/3

Answer 2

To solve the equation $(2x+3)^2 - (2x+5)(2x-5) = 38$, follow these steps:

Step 1: Expand the terms in the equation. Step 2: Simplify the equation. Step 3: Move all terms to one side to set the equation to zero. Step 4: Factorize the quadratic equation. Step 5: Solve for $x$.

Let's go through each step:

Step 1: Expand the terms in the equation. $(2x+3)^2 - (2x+5)(2x-5) = 4x^2 + 12x + 9 - (4x^2 - 25) = 4x^2 + 12x + 9 - 4x^2 + 25$.

Step 2: Simplify the equation. The equation becomes: $12x + 9 + 25 = 38$.

Step 3: Move all terms to one side to set the equation to zero. $12x + 34 = 38$.

Step 4: Move constant term to the other side. $12x = 38 - 34$.

Step 5: Solve for $x$. $12x = 4$.

Now, divide both sides by 12 to isolate $x$: $x = \frac{4}{12} = \frac{1}{3}$.

So the solution to the equation is $x = \frac{1}{3}$.