Solve each equation by completing the square 2q^2+8q=3

Divide by 2

q^2+4q=3/2

q^2+4q (4/2) ^2=3/2 + (4/2) ^2

(q+4/2) ^2=3/2+16/4

taking the square root of both side

√ (q+4/2) ^2=√ (3/2+16/4)

Note that the square will cancel the square root then you will take LCM on the right hand side

q+4/2=√6+16/4

q+4/2=√22/4

q = - 4/2+-√22/4

q = (-4+_√22/4)