Question

When completing the square on the equation c2 + 110 = 12, the resulting solution is:
It

Answer 1

`c=1` and
`c=-12`

Explanation:

The correct equation is:

`c^2+11c=12`

To solve by completing the square method.

Solution:

We have:

`c^2+11c=12`

In order to solve by completing the square method we will carry out the following operations to the given equation to get a perfect square binomial.

We can write as:

`c^2+2.(11)/(2)c=12`

`c^2+2.(11)/(2)c+((11)/(2))^2-((11)/(2))^2=12`

`(c+(11)/(2))^2-((11)/(2))^2=12` [As
`c^2+2.(11)/(2)c+((11)/(2))^2=(c+(11)/(2))^2`]

Adding both sides by
`((11)/(2))^2`

`(c+(11)/(2))^2-((11)/(2))^2+((11)/(2))^2=12+((11)/(2))^2`

`(c+(11)/(2))^2=12+(121)/(4)`

Taking LCD to add fraction.

`(c+(11)/(2))^2=(48)/(4)+(121)/(4)`

`(c+(11)/(2))^2=(169)/(4)`

Taking square root both sides.

`\sqrt{(c+(11)/(2))^2}=\sqrt{(169)/(4)}`

`c+(11)/(2)=\pm(13)/(2)`

Subtracting both sides by
`(11)/(2)` :

`c+(11)/(2)-(11)/(2)=\pm(13)/(2)-(11)/(2)`

`c=\pm(13)/(2)-(11)/(2)`

So, we have:

`c=(13)/(2)-(11)/(2)` and
`c=-(13)/(2)-(11)/(2)`

`c=(2)/(2)` and
`c=(-24)/(2)`

`c=1` and
`c=-12` (Answer)