Solve by completing the square.

If we consult our steps,

- Clear denominators. Multiply both sides by a common denominator.
- Simplify. Remove parentheses and combine like terms.
- Transpose all terms to one side and leave a 0 on the other.
- Factor.
- Set the factors = 0
- Solve.
- Check.

we are ready to transpose known terms to one side and unknown terms to the other

2*x*^{2} - *x* = 10

Next, divide both sides by the coefficient of the square term.

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

Take square roots of both sides.

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.