Solving Quadratic Equations
You have learned to solve quadratic equations by four different methods: the
evenroot property, factoring, completing the square, and the quadratic formula.
The evenroot property and factoring are limited to certain special equations, but
you should use those methods when possible. Any quadratic equation can be solved
by completing the square or using the quadratic formula. Because the quadratic formula
is usually faster, it is used more often than completing the square. However,
completing the square is an important skill to learn.
Methods for Solving ax^{2} + bx + c = 0
Method 
Comments 
Examples 
Evenroot property 
Use when b = 0. 
(x  2)^{2} = 8 x  2 =
Â±

Factoring 
Use when the polynomial can be factored. 
x^{2} + 5x + 6 = 0 (x + 2)(x + 3) = 0 
Quadratic
formula 
Solves any quadratic equation 
x^{2} + 5x + 3 = 0

Completing the square 
Solves any quadratic equation, but quadratic formula is faster 
x^{2}  6x + 7 = 0 x^{2} 
6x + 9 = 7 + 9
(x  3)^{2} = 2 
Helpful hint
If our only intent is to obtain
the answer, then we would
probably use a calculator that
is programmed with the quadratic
formula. However, by
learning different methods,
we gain insight into the problem
and get valuable practice
with algebra. So be sure you
learn all of the methods.
