Solving a Quadratic Equation
by Using the Quadratic Formula
Remember those equations that you were told were un-factorable or prime, and thus could not
be solved? Take for example: x 2  10 x  7  0
You cannot solve this equation unless you use either Completing the Square, or the Quadratic
Formula (see Math handout # 23 on Completing the Square). One of the desirable qualities of
the quadratic formula is that, like all formulas, you just plug numbers into it, and then follow
the order of operations until it is solved. You will need to memorize the Quadratic Formula.
 b  b 2 4ac
x
2a
This is the Quadratic Formula
Follow the steps outlined below when using the Quadratic Formula:
Step 1: In order to use the quadratic formula, the equation must be in descending order, and set
to “0”.
Step 2: Label each of the coefficients using “a”, “b”, and “c”.
In our example
x 2  10 x  7  0
a  1 b  10 c  7
Step 3: Plug the values of a, b, and c into the formula
x
  10 
 102 417
21
Step 4: Follow the order of operations to solve for “x”.
x
10  100  28
2
x
10  72
2
72
2
x
10  6 2
2
x  5  3 2 and x  5  3 2
The Academic Support Center at Daytona State College (Math 24 pg 1 of 2)
36
If the number under the radical is
not a perfect square, try to break it
down so that the number under
radical can be reduced.
Solving a Quadratic Equation
by Using the Quadratic Formula (continued)
x
This is the Quadratic Formula
 b  b 2 4ac
2a
Follow the steps outlined below when using the Quadratic Formula:
Step 1: In order to use the quadratic formula, the equation must be in descending order, and set
to “0”.
Step 2: Label each of the coefficients using “a”, “b”, and “c”.
In our example
3x 2  5 x  1  0
a  3 b  5 c  1
Step 3: Plug the values of a, b, and c into the formula
x
  5 
 52 43 1
23
Step 4: Follow the order of operations to solve for “x”.
x
5  25  12
6
x
5  37
6
x
5  37
6
and
x
The Academic Support Center at Daytona State College (Math 24 pg 2 of 2)
5  37
6