May 23rd

May 23rd

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.