Question

What are the solutions of the quadratic equation (x – 8)2 – 13(x – 8) + 30 = 0? Use u substitution to solve.
x = –11 and x = –18
x = –2 and x = 5
x = 2 and x = –5
x = 11 and x = 18

Answer 1

Let u = x − 8. Then u^2 − 13u + 30 = 0.
Factor: (u − 10)(u − 3) = 0, so u = 10 or u = 3.
Back-substitute: x − 8 = 10 ⇒ x = 18; x − 8 = 3 ⇒ x = 11.

So x = 11 and x = 18 (the last choice).