Respuesta :

Answer:

Missing constant: 100

Step-by-step explanation:

perfect square  (a - b)^2 = a^2 - 2ab + b^2

In this case

20x = 2 * x * 10

and

10^2 = 100

so

(x - 10)^2 = x^2 - 20x + 100

An equation with missing terms will have some of its terms removed.

The missing term that makes [tex]x^2 - 20[/tex] a perfect square is 100

The following step will calculate the missing term.

Represent the coefficient of x with k.

So, we have:

[tex]k = -20[/tex]

Divide both sides by 2

[tex]\frac k2 = -10[/tex]

Square both sides

[tex](\frac k2)^2 = (-10)^2[/tex]

[tex](\frac k2)^2 = 100[/tex]

This implies that, the missing term is 100

So, the complete equation is: [tex]x^2 -20x + 100[/tex]

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