Answer:
Step-by-step explanation:
[tex]x^{2}-7x+c=(x+a)^{2}[/tex]
First, multiply out the brackets:
[tex]x^{2}-7x+c=x^{2}+2ax+a^2[/tex]
Now equate the coefficients of [tex]x[/tex] to find [tex]a[/tex]:
[tex]-7=2a[/tex]
⇒ [tex]a=-\frac{7}{2} [/tex]
Now equate the constants using your found value of [tex]a[/tex] to find [tex]c[/tex]:
[tex]c=a^{2}[/tex]
⇒ [tex]c=(-\frac{7}{2} )^{2}=\frac{49}{4}=12.25[/tex]
