From the problem :
[tex]\begin{gathered} 2x^2+7x+3=0 \\ \end{gathered}[/tex]We need to have a perfect square trinomial, rewriting the equation :
[tex]\begin{gathered} (2x^2+7x)+3=0 \\ (2x^2+7x+c)+3=0+c \end{gathered}[/tex]We will add a term c to both sides of the equation.
Factor out 2 so that the coefficient of x^2 will be 1
[tex]2(x^2+\frac{7}{2}x+\frac{c}{2})+3=0+c[/tex]The term c/2 will be equal to the value of half the middle term and squared.
So this will be :
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