Question

5(2x+1)^2-2(3x+2)(3x-2)=(2x+6)(x-6)-11

Answer 1

=$5\left ( 2x+1 \right )^2-2\left ( 3x+2 \right )\left ( 3x-2 \right )=\left ( 2x+6 \right )\left ( x-6 \right )-11\\20x^2+20x+5-18x^2+12x-12x+8-2x^2+6x+36+11=0\\26x+60=0\Rightarrow x=-\frac{30}{13}$

Answer 2

Let's solve the given equation step by step:

5(2x+1)^2 - 2(3x+2)(3x-2) = (2x+6)(x-6) - 11

First, we'll expand and simplify both sides of the equation:

On the left side: 5(2x+1)^2 expands to 5(4x^2 + 4x + 1) = 20x^2 + 20x + 5 2(3x+2)(3x-2) expands to 2(9x^2 - 4) = 18x^2 - 8

So, the left side simplifies to 20x^2 + 20x + 5 - (18x^2 - 8).

On the right side: (2x+6)(x-6) expands to 2x^2 - 12x + 6x - 36 = 2x^2 - 6x - 36 So, the right side simplifies to 2x^2 - 6x - 36 - 11.

Now, we can rewrite the equation with these simplifications:

20x^2 + 20x + 5 - (18x^2 - 8) = 2x^2 - 6x - 36 - 11

Now, combine like terms on both sides of the equation:

20x^2 + 20x + 5 - 18x^2 + 8 = 2x^2 - 6x - 36 - 11

Simplify further:

(20x^2 - 18x^2) + 20x + 5 + 8 = 2x^2 - 6x - 36 - 11

2x^2 + 20x + 13 = 2x^2 - 6x - 47

Now, let's isolate the variables by moving all terms involving x to one side and constants to the other side:

2x^2 - 2x^2 + 20x + 6x = -47 - 13

Combine like terms:

26x = -60

Now, divide both sides by 26 to solve for x:

x = -60 / 26

Simplify the fraction:

x = -30 / 13

So, the solution to the equation is:

x = -30/13