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x^2-20x +c

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1 Answer

Completing the square involves equations of the form:

ax2 + bx + c

where c = (b/2)2

so whatever the "b" value is simply divide it by two and then square that number

in your case you have

-20 applying that formula gives you (-20/2)2 = 100

so your answer is c = 100

your polynomial is

x2 - 20x + 100

and that factors to

(x - 10)2

multiplying that out you get:

(x - 10)*(x - 10)

x2 - 10x - 10x + 100

x2 - 20x + 100

 

I'll answer one of your other questions to further this example, you are asked to find the perfect square of

x2 - 2.2x + c

Again just divide -2.2 by 2, then square that number and add it to both sides of the equation (if they give you an equation)

(-2.2/2) = -1.1 and then (-1.1)2 = 1.21

so c = 1.21

your polynomial is

x2 - 2.2x + 1.21

and that factors to

(x - 1.1)2

multiply it out to check and you'll find

(x - 1.1)*(x - 1.1)

x2 - 1.1x - 1.1x + 1.21