Methods for Solving Quadratic Equations
Quadratic equations are of the form ax + bx + c = 0, where a  0
Quadratics may have two, one, or zero real solutions .
1. Factoring
Set the equation equal to zero. If the quadratic side is
factorable, factor, then set each factor equal to zero.
Example: x = -5x - 6
| Move all terms to one side |
x +5x + 6 = 0 |
| Factor |
(x + 3)(x + 2) = 0 |
| Set each factor to zero and
solve |
x + 3 = 0 x = -3
|
x + 2 = 0 x = -2
|
2. Principle of Square Roots
If the quadratic equation involves a SQUARE
and a CONSTANT (no first degree term), position
the square on one side and the constant on the other side. Then
take the square root of both sides. (Remember, you cannot take
the square root of a negative number, so if this process leads to
taking the square root of a negative number, there are no real
solutions.)
Example 1: x - 16 = 0
| Move the constant to the right side |
x = 16 |
| Take the square root of both
sides |
 x = ± 4, which means x = 4 and
x = -4
|
Example 2: 2(x + 3)- 14 = 0
|
