Question

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

Answer 1

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

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.

Answer 2

The answer is

`(x+4)^2=-6`

Explanation:

Follow the steps below.

1) Take common factor 10

`10(x^2 + 8x + 22) = 0`

2) For an equation of the form
`ax ^ 2 + bx + c`

Calculate
`((b)/(2))^2`

In this case the equation is
`x^2 + 8x + 22= 0`

`a=1\\b=8\\c =22\\\\((b)/(2))^2 = ((8)/(2))^2 = 16`

3) Add 16 on both sides of equality

`10(x^2 + 8x + 16) +220= 16*10`

4) Factor the expression into parentheses and simplify

`10(x+4)^2 +220= 16*10`

`10(x+4)^2= 16*10-220`

`10(x+4)^2 =-60`

`(x+4)^2 =-6`