Question

Write x^2+8x+19 in the form (x+c)^2+d

Answer 1

To write the expression x^2 + 8x + 19 in the form (x + c)^2 + d, we need to complete the square.

First, we add and subtract the square of half the coefficient of x from the expression:

x^2 + 8x + 19 = (x^2 + 8x + 16) + 3

Next, we rewrite the first part of the expression as a perfect square trinomial:

x^2 + 8x + 16 = (x + 4)^2

Therefore, the expression can be written in the form (x + c)^2 + d as:

x^2 + 8x + 19 = (x^2 + 8x + 16) + 3
= (x + 4)^2 + 3

So, (x^2 + 8x + 19) can be written in the form (x + 4)^2 + 3.

Answer 2

`x^(2) + 8x+19=0`
shift 19 to other side

`x^(2) +8x = -19`
take constant term of 'X' AND DIVIDE BY 2 ALSO SQUARE IT

`4^(2)`
add
`4^(2)` to both sides

`x^(2) +8x +4^(2)= -19 +4^(2)`

`(x+4 )^2 = -3`

`(x+4 )^(2) +3 =0`

Explanation:

see if its correct?