How do you solve k^2-6k+8=0k26k+8=0 by completing the square?

2 Answers
Jun 16, 2018

k=2" or "k=4k=2 or k=4

Explanation:

"subtract 8 from both sides"subtract 8 from both sides

k^2-6k=-8k26k=8

k^2+2(-3)k color(red)(+9)=-8color(red)(+9)k2+2(3)k+9=8+9

(k-3)^2=1(k3)2=1

color(blue)"take square root of both sides"take square root of both sides

k-3=+-1larrcolor(blue)"note plus or minus"k3=±1note plus or minus

k=3+-1k=3±1

k=3-1=2" or "k=3+1=4k=31=2 or k=3+1=4

Jun 16, 2018

k=4, k=2k=4,k=2

Explanation:

First lets complete the square:

k^2-6k+8=0k26k+8=0

rArr (k-3)^2-9+8=0(k3)29+8=0

therefore (k-3)^2=-1

rArr (k-3)^2=1

k-3=pmsqrt1

k=3pm1

k=4, k=2