Question

(2x-1) (2x+1)- (2x+3) ^2=38

Answer 1

4 x^2 + 2x - 2x - 1 - 4 x^2 + 12x + 9 =  38;
12x + 8 = 38;
12x = 30;
x = 12/30 = 2/5;

Answer 2

(2x-1)(2x+1)-(2x+3)²=38
4x²-1-(2x+3)²=38
4x²-1-4x²-12x-9=38
-1-12x-9=38
-12x-10=38
-12x-48=0
-12x=48
x=48/-12=-4.

Answer 3

To solve the equation, let's first expand and simplify the expression on the left-hand side:

(2x - 1)(2x + 1) - (2x + 3)^2 = 38

Expanding (2x - 1)(2x + 1): = 4x^2 + 2x - 2x - 1

Simplifying: = 4x^2 - 1

Expanding (2x + 3)^2: = (2x + 3)(2x + 3) = 4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9

Now, the equation becomes: 4x^2 - 1 - (4x^2 + 12x + 9) = 38

Let's continue simplifying: 4x^2 - 1 - 4x^2 - 12x - 9 = 38

The x^2 terms cancel out: -1 - 12x - 9 = 38

Combine constants: -12x - 10 = 38

Now, isolate the variable: -12x = 38 + 10 -12x = 48

Divide both sides by -12: x = 48 / -12 x = -4

So, the solution to the equation is x = -4. Let's verify this by substituting the value of x back into the original equation:

(2x - 1)(2x + 1) - (2x + 3)^2 = 38

(2(-4) - 1)(2(-4) + 1) - (2(-4) + 3)^2 = 38

(-8 - 1)(-8 + 1) - (-8 + 3)^2 = 38

(-9)(-7) - (-5)^2 = 38

63 - 25 = 38

38 = 38

The equation holds true for x = -4. So, the solution is verified.