What number must you add to complete the square x^2+4x=15

Since we want it in the form: (x - a) ², let's first expand (x - a) ² and then equate for the coefficients.

(x - a) ² = x² - 2ax + a²

x² + 4x - 15 = x² - 2ax + a²

Now, let's focus on the middle term.

4x = - 2ax

4 = - 2a

a = - 2

Thus, we know that a = - 2

Then, we can say (x + 2) ² = x² + 4x - 15

x² + 4x + 4 = x² + 4x - 15

Thus, 19 units are needed in order to complete the square to produce:

(x + 2) ²