answer
10
step-by-step explanation
first find the (x+a)^2 part
using x^2 + 6x + c, we need to find the value c that completes the perfect square
to do this, divide 6 by two to find a in (x+a)^2
6/2 = 3 = a
c = a^2
c = 3^2 = 9
plug in values
x^2 + 6x + 9 = (x+3)^2
compare this to x^2 + 6x − 1, and you can see there is a (9 - -1) = 10 difference, so subtract 10 from both sides
x^2 + 6x + 9 = (x+3)^2
x^2 + 6x + 9 - 10 = (x+3)^2 - 10
x^2 + 6x + - 1 = 0 = (x+3)^2 - 10
0 = (x+3)^2 - 10
(x+3)^2 = 10
k = 10
