Answer:
we would add [tex]\:\left(\frac{1}{2}\right)^2\:[/tex] or 1/4 to make the expression a perfect square.
Step-by-step explanation:
Given the expression
[tex]x^2+x[/tex]
[tex]\mathrm{Write}\:x^2+x\:\mathrm{in\:the\:form:\:\:}x^2+2ax+a^2[/tex]
[tex]2a=1[/tex]
Divide both sides by 2
[tex]\frac{2a}{2}=\frac{1}{2}[/tex]
[tex]a=\frac{1}{2}[/tex]
as
[tex]x^2+2ax+a^2=\left(x+a\right)^2[/tex]
[tex]\mathrm{Add\:}\:\left(\frac{1}{2}\right)^2\:[/tex]
[tex]x^2+1x+\left(\frac{1}{2}\right)^2=\left(x+\frac{1}{2}\right)^2[/tex]
Thus, we would add [tex]\:\left(\frac{1}{2}\right)^2\:[/tex] or 1/4 to make the expression a perfect square.
