Answer:
[tex] {x}^{2} + 7x + \frac{49}{4} = {(x + \frac{7}{2}) }^{2} [/tex]
Explanation:
[tex] {x}^{2} + 7x + a = {(x + b)}^{2} [/tex]
[tex] {x}^{2} + 7x + a = {x}^{2} + 2bx + {b}^{2} [/tex]
compare the x co-efficient
[tex] 7 = 2b[/tex]
[tex] b = \frac{7}{2} [/tex]
compare the constants
[tex]a = {b}^{2} [/tex]
[tex]a = {( \frac{7}{2}) }^{2} [/tex]
[tex]a = \frac{49}{4} [/tex]
