How do i solve z^2+9=10z

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