Answer:
z = 1, z = 9
Step-by-step explanation:
Given
z² + 9 = 10z ( subtract 10z from both sides )
z² - 10z + 9 = 0
Consider the factors of the constant term (+ 9) which sum to give the coefficient of the z- term (- 10)
The factors are - 1 and - 9, since
- 1 × - 9 = 9 and - 1 - 9 = - 10, thus
(z - 1)(z - 9) = 0 ← in factored form
Equate each factor to zero and solve for z
z - 1 = 0 ⇒ z = 1
z - 9 = 0 ⇒ z = 9
