Quadratic Equations and Factoring

Question

Decide the value of k if x^2-2(k+1)x+k+7 can be factored as a perfect square.

Answer 1

x^2 +(2k+1)x + k = -7

x^2 +(2k+1)x + (k+1/2)^2 = -7-k + (k+1/2)^2

(x + k + 1/2)^2 = -7-k + k^2 +k + 1/4

x+k+1/2 = +/- square root of (k^2 -27/4)

x = k+1/2 when k^2-27/4 = 0, k=+/-sqr(27)/2

k= about 2.6 or -2.6

x^2 + (6.2)x + 2.6 + 7

= (x+3.1)^2 + -3.1^2 +2.6+7

= about (x+3.1)^2 +0

= a perfect square: (x+3.1) squared