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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