I think this is an odd question.
Usually completing the square is done as a quadratic equation solving technique.
But if you just want to know what constant needs to be added to make it a perfect square then this is what I'd do.
(it is very similar to what heureka has done)
4x2−4x−27=4(x2−x−274)=4(x2−1x+14−284)=4(x2−1x+14−284)=4(x2−1x+14)−28=22(x2−12x+14)−28=22(x−12)2−28=(2(x−12))2−28=(2x−1)2−28
So the expression would be a perfect square if 28 were added.
4x2−4x−27=4(x2−x)−27=4(x2−x+(12)2−(12)2)−27=4((x−12)2−14)−27=4(x−12)2−44−27=4(x−12)2−1−27=4(x−12)2−28
.I think this is an odd question.
Usually completing the square is done as a quadratic equation solving technique.
But if you just want to know what constant needs to be added to make it a perfect square then this is what I'd do.
(it is very similar to what heureka has done)
4x2−4x−27=4(x2−x−274)=4(x2−1x+14−284)=4(x2−1x+14−284)=4(x2−1x+14)−28=22(x2−12x+14)−28=22(x−12)2−28=(2(x−12))2−28=(2x−1)2−28
So the expression would be a perfect square if 28 were added.