Question

Complete the square on the following quadratic

x^2+16x+9=0

After removing C, what value is added to both sides of the equation?

Answer 1

Completing the square we have

`x_(1) =√(55)-8\\\\x_(2)=-√(55)-8`

Explanation:

`x^(2) +16x+9=0`

we have to divide the coefficient of x by half, and then raise it to the square, that number is added and subtracted at the same time

`x^(2)+16x+64-64+9=0`

`(x+8)^(2) -55=0`

`(x+8)^(2) =55`

later we can write

`\sqrt{(x+8)^(2)}= √(55)`

we know

`\sqrt[2]{a^(2)} =abs(a)`

so we have

abs(x+8)=
`√(55)`

we have

`x_(1) =`x+8=
`√(55)`

`x_(2)=`x+8=
`-√(55)`

finally we have

`x_(1)=√(55)-8`

`x_(2) = -√(55)-8`