Answer:
4
Step-by-step explanation:
In completing the square, c is given by [tex](\frac{b}{2})^2[/tex]
Given,
[tex]x^{2} -4x+c[/tex]
a = 1, b = -4, c = ?
[tex]x^{2} -4x+(\frac{b}{2} )^2[/tex]
Since b = -4, substitute
[tex]x^2 - 4x + (\frac{-4}{2})^2[/tex]
[tex]x^2 - 4x + (-2)^2[/tex] ---> Simplify
[tex](-2)^2 = 4[/tex]
[tex]x^2 - 4x + 4[/tex] = [tex](x - 2)^{2}[/tex]
Therefore, 4 must be added to [tex]x^{2} - 4x[/tex] for it to be perfect square trinomial.
