complete the square

[limber token]

<@&791435371564892232>

[gilded valve]

complete the square

Well factor out a 3 from the first 2 terms

3(x² + 4x) + 19

then complete the square from what's inside that

then bring the 3 back by multiplying it back in and simplify

[limber token]

3(x+2)^2 + 5.5?

[gilded valve]

should be 3[(x + 2)² - 4] + 19
then expand back the 3
3(x + 2)² - 12 + 19
so 3(x + 2)² + 7

typo 💀

[limber token]

ah i see but why is it -4 instead of 4?

[gilded valve]

cause if we expanded it

We originally had x² + 4x right

[limber token]

yh

[gilded valve]

if we expanded (x + 2)²

we would get x² + 4x + 4

so we want to remove that 4

to just keep x² + 4x

[limber token]

ohh makes sense. thanks