Solving Quadratic Equations
by Completing the Square
Recall that x + 6 x + 9 is a trinomial square since ( x
+ 3 ) are its factors. Note that 3 is half of
six.
Notes on Completing the Square
Completing the square is a procedure used to determine a
solution of an equation by rewriting the equation as a trinomial
square equal to a rational number.
Steps to solving quadratic equations by completing the
square:
1. Isolate the variable terms on one side of the equation.
2. Divide both sides of the equation by the coefficient of
x . (This is not needed if the coefficient
is 1.)
3. Determine the value needed to complete the square by
dividing the coefficient of x by 2 and squaring the result.
4. Add the value obtained to both sides of the equation.
5. Rewrite the trinomial as a binomial square. 6. Use the
principle of square roots to determine the possible solutions and
solve.
