Question

When completing the square, what value must you add to both sides of the equation to create a perfect square trinomial?

Answer 1

Notice that half of the coefficient of x is (1/2)(-4), or -2.

Then x^2 - 4x   becomes
         x^2 - 4x + 4 - 4 = 0, or (x -2)^2 = 4.   Then x = -2 plus or minus 2, and the two roots are 0 and -4.

Thus, add 4 to both sides to obtain x^2 - 4x + 4 = 4.