Answer:
The value of k is 4 and q is 16.
Step-by-step explanation:
First, you have to expand the brackets by applying :
[tex] {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]
[tex] {x}^{2} + 8x + q = {(x + k)}^{2} [/tex]
[tex] {x}^{2} + 8x + q = {x}^{2} + 2kx + {k}^{2} [/tex]
Next, you have to do it by comparison :
[tex] {x}^{2} + 8x + q = {x}^{2} + 2kx + {k}^{2} [/tex]
[tex]by \: comparison[/tex]
[tex]8x = 2kx[/tex]
[tex]8 = 2k[/tex]
[tex]k = 4[/tex]
[tex]q = {k}^{2} [/tex]
[tex]q = {4}^{2} [/tex]
[tex]q = 16[/tex]
