For a 2×2 matrix acbd, the determinant is:
ad−bc
Calculate the left side determinant:
x48x
=x×x−8×4
=x2−32
Calculate the right side determinant:
61826
=6×6−2×18
=36−36
=0
Since the determinants are equal:
x2−32=0
x2=32
x=±32
Simplify 32:
32=16×2
=16×2
=42
Therefore, x=±42