Question

(х-3)(х+3)=(2х-3)2-18​

Answer 1

Ответ:

x²-3²=4x-6-18

x-4x=-18(-6)+9

5x=-15

x=-15:5

x=3

Answer 2

To solve the equation (x - 3)(x + 3) = (2x - 3)^2 - 18, you can start by simplifying both sides of the equation:

(x - 3)(x + 3) = (2x - 3)^2 - 18

Expand the left side of the equation using the difference of squares formula (a^2 - b^2 = (a + b)(a - b)):

(x - 3)(x + 3) = [(2x - 3)(2x - 3)] - 18

Now, expand both sides further:

(x^2 - 9) = (4x^2 - 12x + 9) - 18

Now, simplify the equation:

x^2 - 9 = 4x^2 - 12x + 9 - 18

Combine like terms:

x^2 - 9 = 4x^2 - 12x - 9

Now, move all terms to one side of the equation:

x^2 - 4x^2 + 12x - 9 + 9 = 0

Combine the x^2 and -4x^2 terms:

-3x^2 + 12x = 0

Now, factor out -3x from both terms:

-3x(x - 4) = 0

Now, set each factor equal to zero:

-3x = 0 or x - 4 = 0

Solve for x in each equation:

1. -3x = 0 x = 0

2. x - 4 = 0 x = 4

So, the equation has two solutions: x = 0 and x = 4.