6.

 

Solve by completing the square.

1. Divide both sides by the coefficient of the square term.

2. Transpose known terms to one side and unknown terms to the other. A term is an unknown term if it has a factor of the unknown x in it and it is a know term if it doesn't.

3. Add the square of half the coefficient of the first degree term to both sides. The coefficient of the first degree term is 1/2. Half of that is 1/4. The square of that is 1/16. We add 1/16 to both sides.

On the right we are adding fractions, so we need common denominators. The common denominator is 16. We need to multiply both the top and bottom of the 5 by 16.

4. Simplify

5. Take square roots of both sides.

6. Add 1/4 to both sides

This gives 2 answers

or

which are the two answers we got by factoring. To see the checks, see the discussion of solving this problem by factoring.

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