Question

What number must you add to complete the sqaure? x^2+2x=-1

Answer 1

1

Explanation:

By adding 1 on both sides we get:

`x^2+2x+1 = -1+1 = 0`

By adding such we get on the left a perfect square trinomial (a trinomial that is the result of squaring a binomial):

`x^2 +2x+1 = (x+1)^2`

To decide what to add, understand what is the result of squaring a binomial of the form:
`(x+c)\\(x+c)^2 = (x+c)(x+c) = x^2 +2*c*x + c^2`

In your case, 2*c*x is "2x" therefore the value of c must be 1.

so to complete the square you need to add
`c^2` which will result in
`1^2= 1`