+33653 Rearrange the equation to look like:
x^2 -2(2k+1)x + k+2 = 0
This has equal roots when the discriminant is zero.
(In general, when a*x^2 + b*x + c = 0, the discriminant is b^2 - 4*a*c):
(-2(2k + 1))^2 - 4*1*(k+2) = 0
4*(2k+1)^2 - 4*(k+2) = 0
(2k+1)^2 - (k+2) = 0
4k^2 + 4k + 1 - k - 2 = 0
4k^2 + 3k - 1 = 0
(4k - 1)(k + 1) = 0
4k = 1 or k = -1
k = 1/4 or k = -1
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