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

2 Answers
Jim G.
Jun 16, 2018

#k=2" or "k=4#

Explanation:

#"subtract 8 from both sides"#

#k^2-6k=-8#

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

#(k-3)^2=1#

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

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

#k=3+-1#

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

Brandon
Jun 16, 2018

#k=4, k=2#

Explanation:

First lets complete the square:

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

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

#therefore# #(k-3)^2=-1#

#rArr (k-3)^2=1#

#k-3=pmsqrt1#

#k=3pm1#

#k=4, k=2#

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