Х² - 36 = 0 3х² - 9х = 0 9х² = 54х Х² - 15 = 2х Х² + 4х = 5

To solve the first equation, we can factor it as a difference of squares:

x² - 36 = 0 (x - 6)(x + 6) = 0

Setting each factor equal to zero, we get:

x - 6 = 0 or x + 6 = 0

Solving for x in each case, we find:

x = 6 or x = -6

So the solutions to the first equation are x = 6 and x = -6.

Moving on to the second equation:

3x² - 9x = 0

Factoring out the greatest common factor of 3x, we have:

3x(x - 3) = 0

Setting each factor equal to zero, we get:

3x = 0 or x - 3 = 0

Solving for x in each case, we find:

x = 0 or x = 3

So the solutions to the second equation are x = 0 and x = 3.

For the third equation:

9x² = 54x

Dividing both sides by 9x (ensuring we are not dividing by zero), we have:

x = 6

So the solution to the third equation is x = 6.

Moving on to the fourth equation:

x² - 15 = 2x

Rearranging the terms, we have:

x² - 2x - 15 = 0

Factoring this quadratic equation, we find:

(x - 5)(x + 3) = 0

Setting each factor equal to zero, we get:

x - 5 = 0 or x + 3 = 0

Solving for x in each case, we find:

x = 5 or x = -3

So the solutions to the fourth equation are x = 5 and x = -3.

Lastly, for the fifth equation:

x² + 4x = 5

Rearranging the terms, we have:

x² + 4x - 5 = 0

Factoring this quadratic equation, we find:

(x + 5)(x - 1) = 0

Setting each factor equal to zero, we get:

x + 5 = 0 or x - 1 = 0

Solving for x in each case, we find:

x = -5 or x = 1

So the solutions to the fifth equation are x = -5 and x = 1.