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

Move the constant to the other side	2(x + 3)=14
Isolate the square	(x + 3) = 7 (divide both sides by 2)
Take the square root of both sides
Solve for x	This represents the exact answer. Decimal approximations can be found using a calculator.