1. ## complete the square

Hi everyone,

I don't remember how to complete the square with a -x^2. Could you please explain to me how to complete the square of 6+4x-4x^2?

Thank you

2. Originally Posted by chocolatelover
explain to me how to complete the square of 6+4x-4x^2?
$6+4x-4x^2=7-(1-4x+4x^2)=7-(1-2x)^2$

3. Originally Posted by chocolatelover
Hi everyone,

I don't remember how to complete the square with a -x^2. Could you please explain to me how to complete the square of 6+4x-4x^2?

Thank you
Here is one way.

Remember, you "complete the square" only when the coefficient of the squared variable is 1.

6 +4x -4x^2
= -4x^2 +4x +6
= -4(x^2 -x) +6
Now, complete the square,
= -4(x^2 -x +(-1/2)^2 -(-1/2)^2) +6
= -4[(x -1/2)^2 -1/4] +6
= -4(x -1/2)^2 +1 +6
= -4(x -1/2)^2 +7