3. 2x2 - x - 10 = 0

Solve by completing the square.

If we consult our steps,

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

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

2x2 - x = 10

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

x2 - x/2 = 5

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


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