 Square Root Property
 We have been using only principal square roots,
but now we'll start using both the positive and negative square root.
 The square root property is that if
, where a
is a real number, then
.

Example: 
Solve (x  3)^{2} = 4. 


x  3 = ±2 
Square root property 

x = 3 ± 2 
Add 3 to both sides 

x = 3 + 2 or x = 3  2 
Two solutions 

x = 5, 1 
Simplyfying 
 Idea of Completing the Square
 Given the problem
Solve x^{2} + bx + c = 0,
find a number that complets the square of x^{2} + bx to get to an equivalent equation of the form
Solve (x  d)^{2} = f,
that can be solved as in the above example.

 Steps to Solving a Quadratic Equation by Completing the Square

 Make the numerical coefficient of the x^{2} term equal to 1.
 Rewrite the equation with the constant by itself on the right side of the equation.
 Take ½ the numerical coefficient of the x term, square it, and add this
quantity to both sides of the equation.
 Factor the trinomial into the square of a binomial.
 Use the square root property to take the square root of both sides of the equation.
 Solve for x.
 Check the solution in the original equation.
 Note that the variable was called "x" in the above steps, but it can be called by any variable name, not necessarily just x.
