2x^2+8x+3 in the form 2 (x+p) ^2+q

2 (x+2) ^2-5

Step-by-step explanation:

2 (x+p) ^2+q

=2 (x^2+2px+q^2) + q

=2x^2+4px+2p^2+q

Comparing coefficients with the 2x^2+8x+3

4p=8, p=2

2p^2+q=3, Solving for q given p, q=-5

Substituting values of p and q,

2 (x+2) ^2-5