Explain why the equation (x-6) ^-13=12 has two solutions. Then solve the equation to find the solutions. Show your work.

x = 10 and x = (-2) are the solutions.

Step-by-step explanation:

In the given equation (x - 4) ² - 28 = 8

we will first find the zero factors which will further decide the number of solutions.

(x - 4) ² - 28 = 8

(x - 4) ² - 28 - 8 = 8 - 8 (By subtracting 8 on both the sides of the equation)

(x - 4) ² - 36 = 0

(x - 4) ² - 6² = 0

(x - 4 - 6) (x - 4 + 6) = 0

(x - 10) (x + 2) = 0

Now the equation only two zero factors or two solutions.

x = 10 and x = - 2

Answer is two solutions only x = 10 and x = (-2)