Question

How do you solve `m^2 - 4m -32 = 0` by completing the square?

Answer 1

Solve m^2 - 4m - 32 = 0. There are 2 ways:
Find 2 numbers knowing their sum (-b = 4) and their product (c = -32).
Compose factor pairs of (-32), and apply the Rule of Signs. Roots have different signs since a and c have different signs. Proceed: (-1, 32)(-2, 16)(-4, 8). This last sum is ( -4 + 8 = 4 = -b). Then the 2 real roots are: -4 and 8. No need for factoring or completing the squares.

Completing the squares.
`f(m) = m^2 - 4m + 4 - 4 - 32 = 0`

f(m) = (m - 2)^2 - 36 = 0
= (m - 2 - 6)(m -2 + 6)#

(m - 2 - 6) = 0 --> m = 8
(m - 2 + 6) = 0 --> m = -4