x^2-20x +c

Question

Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square.

Answer 1

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