A quadratic equation is an equation of the form (y = ax + bx + c).  When graphed, a quadratic equation appears as a parabola.  To solve for x in a quadratic equation, you must first make sure that y = 0.  Then you can use one of two methods: factoring or the Quadratic Formula.

To solve using the Quadratic Formula, substitute for a, b, and c in the following equation: 0 =  The  symbol means you must add and subtract the radical value; this will often result in two separate solutions.  However, there are certain cases where you will find one or even zero solutions.

The factoring method can be used only in certain situations. To use this method, you express the quadratic equation as a multiplication of two binomials.  Remember that when two quantities are multiplied for a result of 0, one of the quantities must equal 0.  Therefore, if you have a multiplication like (x - 5)(x + 3), x must be equal to 5 or -3.

(1)  Solve the following quadratic equation using the Quadratic Formula:  -4 = x+ 5x
(2)  Solve this equation here, using the factoring method:  0 = x- x - 6
(3)  Determine which method is more appropriate, and use it to solve:  0 = x+ 25x - 21