Use the technique of completing the square to transform the quadratic equation into the form (x + c)2 = a.

10x2 + 80x + 220 = 0

select the best answer from the choices provided

f(x) = 10 [ (x + 4)^2 = -6 ]

Step-by-step explanation:

Please use " ^ " to indicate exponentation.  Thanks.

Also, please share the possible answer choices.  "Select the best answer from the choices provided."

Start with f(x) = 10x^2 + 80x + 220 = 0

Factor out the 10 to simplify this "completing the square."

f(x) =  10(x^2 + 8x + 22) = 0

Complete the square of x^2 + 8x + 22 only, for now.

Identify the coefficient of the x term.  It is 8.  Take half of that (it is 4) and square your result:  16

Now add 16 to x^2 + 8x  and then subtract 16 from that sum:

x^2 + 8x + 16 - 16 + 22 = 0, or

x^2 + 8x + 16      + 6     = 0

Rewrite x^2 + 8x + 16  as (x + 4)^2

and then the whole expression x^2 + 8x + 16 - 16 + 22 as (x + 4)^2 = -6

Finally, rewrite this as

f(x) = 10 [ (x + 4)^2 = -6 ] which is the desired form of the original equation.

The answer is

Step-by-step explanation:

Follow the steps below.

1) Take common factor 10

2) For an equation of the form

Calculate

In this case the equation is

3) Add 16 on both sides of equality

4) Factor the expression into parentheses and simplify