Solving Quadratic Equations by Completing the Square
Objective Learn the technique of completing
the square, and how to use this technique to solve quadratic
equations and to verify the Quadratic Formula.
Completing the square is an important technique in working
with quadratic equations. The technique is motivated by the
simplest example of a quadratic equation, when the square of a
variable is equal to a positive number.
Taking the Square Root of Each Side
Example 1
Solve x^{ 2}  9.
Solution
To solve this equation, simply take the square root of each
side.
You can also use this method to solve a quadratic equation in
which the square of an expression of the form ( x  c ) is equal
to a positive number.
Example 2
Solve ( x  3)^{ 2} = 16.
Solution
Again, take the square root of each side.
These examples show how to solve quadratic equations of the
form ( x + k )^{ 2} = d or ( x + k )^{ 2}  d =
0. This is called completed square form.
Quadratic equations that are not in this form can be rewritten
using a technique called completing the square.
