Question

(3x+2)(3x-2)-(x-3)(x+2)=32

Answer 1

Ответ в закрепленной фотке

Answer 2

To solve the equation, let's expand the given expression and simplify it:

(3x + 2)(3x - 2) - (x - 3)(x + 2) = 32

Expanding the expressions, we have:

(9x^2 - 4) - (x^2 - x - 6) = 32

Removing the parentheses and simplifying further:

9x^2 - 4 - x^2 + x + 6 = 32

Combining like terms:

8x^2 + x + 2 = 32

Rearranging the equation to isolate the quadratic term:

8x^2 + x - 30 = 0

Now we have a quadratic equation in standard form. To solve it, we can use factoring, completing the square, or the quadratic formula. Let's solve it using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 8, b = 1, and c = -30.

x = (-(1) ± √((1)^2 - 4(8)(-30))) / (2(8))

Simplifying further:

x = (-1 ± √(1 + 960)) / 16

x = (-1 ± √961) / 16

x = (-1 ± 31) / 16

This gives us two possible solutions:

x1 = (-1 + 31) / 16 = 30 / 16 = 15/8

x2 = (-1 - 31) / 16 = -32 / 16 = -2

Therefore, the solutions to the equation (3x + 2)(3x - 2) - (x - 3)(x + 2) = 32 are x = 15/8 and x = -2.