Thread: 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

Originally Posted by chocolatelover

explain to me how to complete the square of 6+4x-4x^2?

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
= 7 -4(x -1/2)^2 ----------answer.