How do you complete the square to solve #2k^2 + 2k = 10#?

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Answer 1 · 2015-06-12T05:59:09

Divide by the coefficient of #k^2#, then add the square of half the coefficient of #k# to both sides.

First, divide everything in the equation by two, to make sure that #k^2# has a coefficient of #1#

#k^2+k=5#

Next, add #(1/2)^2# to both sides of the equation

#k^2 + k + (1/2)^2 = 5 + (1/2)^2#

The left hand side is now a perfect square

#(k+1/2)^2 = 5 + (1/2)^2#

Because the right hand side is positive, you can take the #+-sqrt()# of both sides

#k+1/2 = +-sqrt(5 + 1/4#

Simply subtract 1/2 from both sides for your final answer

#k=-1/2+-sqrt(5 1/4)=-1/2+-sqrt(21/4)=-1/2+-sqrt(21)/2#. Finis!