Question

(2х+5)^2—(4 х-1)^2=24

Answer 1

4x²+20x+25-16x²+8x-1-24=0

-12x²+28x=0

3x²-7x=0

x(3x-7)=0

x1= 0               x2= 7/3

Answer 2

Let's solve the given equation step by step:

(2x + 5)^2 - (4x - 1)^2 = 24

First, let's expand both squared terms:

(2x + 5)^2 = (2x + 5)(2x + 5) = 4x^2 + 20x + 25 (4x - 1)^2 = (4x - 1)(4x - 1) = 16x^2 - 8x + 1

Now, replace these expanded terms back into the original equation:

(4x^2 + 20x + 25) - (16x^2 - 8x + 1) = 24

Now, combine the like terms:

4x^2 + 20x + 25 - 16x^2 + 8x - 1 = 24

Next, simplify the equation:

-12x^2 + 28x + 24 = 24

Now, let's set the equation to zero by subtracting 24 from both sides:

-12x^2 + 28x = 0

Now, let's factor out common terms:

4x(-3x + 7) = 0

Now, we have two possibilities for this equation to be true:

1. 4x = 0 This implies x = 0.

2. -3x + 7 = 0 Add 3x to both sides: 7 = 3x

   Divide both sides by 3: x = 7/3

So, the solutions to the equation are x = 0 and x = 7/3. You can check these values by substituting them back into the original equation to ensure they satisfy it.