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

1 Answer
Jun 12, 2015

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

Explanation:

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!