Question

(3x-2)(3x+2)-7x (x+1)=2 (x-1)(x+1)​

Answer 1

(3x-2)(3x+2)-7x(x+1) = 2(x-1)(x+1)​

9x² - 4 - 7x² - 7x = 2(x²-1)

2x²- 7x - 4 = 2x² - 2

-7x = -2+4

-7x = 2

7x = -2

x = -2/7

Answer 2

To solve the given equation, we'll start by simplifying both sides and then finding the value(s) of 'x' that satisfy the equation.

Given equation: (3x-2)(3x+2) - 7x(x+1) = 2(x-1)(x+1)

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

(3x-2)(3x+2) = 9x^2 - 6x + 6x - 4 = 9x^2 - 4

• 7x(x+1) = -7x^2 - 7x

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

Now the equation becomes:

(9x^2 - 4) - (-7x^2 - 7x) = 2x^2 - 2

Step 2: Simplify and combine like terms:

9x^2 - 4 + 7x^2 + 7x = 2x^2 - 2

Combine like terms on the left side:

(9x^2 + 7x^2) + (7x) - 4 = 2x^2 - 2

16x^2 + 7x - 4 = 2x^2 - 2

Step 3: Move all the terms to one side of the equation to set it equal to zero:

16x^2 + 7x - 4 - 2x^2 + 2 = 0

Step 4: Combine like terms again:

14x^2 + 7x - 2 = 0

Now, to solve the quadratic equation, we can use the quadratic formula:

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / 2a

Where a = 14, b = 7, and c = -2.

Step 5: Plug in the values into the quadratic formula:

x = [ -7 ± √(7^2 - 4 * 14 * -2) ] / 2 * 14

Step 6: Simplify further:

x = [ -7 ± √(49 + 112) ] / 28

x = [ -7 ± √161 ] / 28

So the solutions for 'x' are:

1. x = [ -7 + √161 ] / 28
2. x = [ -7 - √161 ] / 28

These are the two values of 'x' that satisfy the original equation.