Factorise 8m2−5m−22 completely.

To factorise the quadratic equation 8m^2 - 5m - 22, we need to find two numbers that multiply to (8*-22) = -176 and add to -5.

The two numbers that satisfy these conditions are -11 and 16.

So, we can rewrite the middle term of the quadratic equation as -11m + 16m.

The equation becomes: 8m^2 - 11m + 16m - 22.

Now, we can factor by grouping:

8m^2 - 11m + 16m - 22 = 8m(m - 11/8) + 16(m - 11/8)

Now, we can factor out (m - 11/8):

8m(m - 11/8) + 16(m - 11/8) = (8m + 16)(m - 11/8)

So, the factorised form of the equation 8m^2 - 5m - 22 is (8m + 16)(m - 11/8).