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
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
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
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