What number should be added to the expression x^2+2x to change it into a perfect square trinomial?

To make x^2 + 2x a perfect square we need to add the term { 2 / (2*1) }^2

which equals 1.

Add 1 to both sides: x^2 + 2x = 8

add 1 to both sides: x^2 + 2x + 1 = 8 + 1 (x + 1)^2 = 9

Take square root on both sides: x + 1 = +/- 3 x = +3 - 1 or x = -3 - 1 x = 2 or x = -4