Question

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

Answer 1

Сразу решения
((2x-1)×2)-(x-3)×(x+3)=2×(2x+3)
(4x-2)-(x^2-9)=4x+6
4x-2-(x^2-9)=4x+6
-2-x^2+9=6
7-x^2=6
-x^2=6-7
-x^2=-1
x^2=1
ответ x1= -1; x2= 1

Answer 2

To solve the equation ((2x-1)^2) - (x-3)(x+3) = 2(2x+3), follow these steps:

Step 1: Expand the expressions on both sides of the equation. Step 2: Simplify the equation. Step 3: Solve for 'x.'

Let's go through each step:

Step 1: Expand the expressions on both sides of the equation.

((2x-1)^2) = (2x-1)*(2x-1) = 4x^2 - 2x - 2x + 1 = 4x^2 - 4x + 1

(x-3)(x+3) = xx + x3 - 3x - 33 = x^2 + 3x - 3x - 9 = x^2 - 9

2(2x+3) = 4x + 6

Step 2: Simplify the equation.

Substitute the expanded expressions back into the original equation:

(4x^2 - 4x + 1) - (x^2 - 9) = 4x + 6

Step 3: Solve for 'x.'

Now, combine like terms:

4x^2 - 4x + 1 - x^2 + 9 = 4x + 6

Simplify further:

3x^2 - 4x + 10 = 4x + 6

Move all terms to one side to set the equation to zero:

3x^2 - 4x - 4x + 10 - 6 = 0

3x^2 - 8x + 4 = 0

Now, we can try to solve for 'x' using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where in our case: a = 3 b = -8 c = 4

x = (8 ± √((-8)^2 - 4 * 3 * 4)) / (2 * 3)

x = (8 ± √(64 - 48)) / 6

x = (8 ± √16) / 6

Now, calculate both solutions for 'x':

1. x = (8 + √16) / 6 = (8 + 4) / 6 = 12 / 6 = 2

2. x = (8 - √16) / 6 = (8 - 4) / 6 = 4 / 6 = 2/3

So, the solutions for the equation are x = 2 and x = 2/3.