Hello!
The answers are:
a) [tex]\frac{49}{4}[/tex]
b) [tex](x+\frac{7}{2})^{2}[/tex]
Why?
First, we need to know that for this case:
[tex]a=1\\2ab=7[/tex]
So,
[tex]b=\frac{7}{2}[/tex]
[tex]b^{2} =(\frac{7}{2})^{2}=\frac{49}{4}[/tex]
We must add [tex]\frac{49}{4}[/tex] to the expression in order to form a perfect square trinomial,
[tex]x^{2} +7x+\frac{49}{4}[/tex]
Writing the trinomial as a binomial square:
[tex](x+\frac{7}{2})^{2}=x^{2}+2*\frac{7}{2}*x+(\frac{7}{2})^{2}=x^{2} +7x+\frac{49}{4}[/tex]
Have a nice day!
