A quadratic equation is an equation where the highest
exponent of the variable is 2.
The equation: ax2 + bx + c = 0 is a quadratic
equation in standard form.
There are several ways to solve a quadratic equation. You
are probably familiar with solving by factoring. Here is an example of this
method.
Example: Solve by factoring 3n2
+ 14n – 5 = 0
In many situations, the quadratic equation is not
factorable. In this section we will look at other methods we can use to solve
quadratic equations.
The Principle of Square Roots:
If we
can write a quadratic equation as:
Where k is a number, then we can take the square root of both sides and get:
or 
When you take the square root, you need to write both + and – square roots.
You can
also write this as: 
Example: Solve the following equations
x2
= 45
x2
= -7
Principle of Square Roots (General Case):
If we can write a quadratic
equation as:
Where k is a number, then we can take the square root of both sides and get:
or 
When you take the square root, you need to write both + and – square roots.
We can write this as: 
Example: Solve the following equations
a) (3n + 1)2 = 25
b) (x – 3)2 = -10
c) 3(2x – 3)2 + 8 = 44 continued
Now try this Practice Quiz
Application Problems
Example: A 50-foot rope hangs from the top
of a flagpole. When pulled taught to its full length, the rope reaches a point
on the ground 18 feet from the base of the pole. Find the height of the pole to
the nearest tenth of a foot.
Example: Find the length of each leg of an
isosceles right triangle that has a hypotenuse of length 5 meters.
Example: Suppose that a 20-foot ladder is
leaning against a building and makes an angle of 60 degrees with the ground.
How far up the building does the top of the ladder reach? Express your answer
to the nearest tenth of a foot.
Now try this Practice Quiz