The *quadratic form* is *ax*^{2} + *bx* + *c* = 0, where *a*, *b*, and *c* are just numbers. All quadratic equations can be expressed in this form, as in the following examples.

- 2
*x*^{2}– 4*x*= 32: This equation can be expressed in the quadratic form as 2*x*^{2}+ (–4*x*) + (–32) = 0. In this case,*a*= 2,*b*= –4, and*c*= –32. *x*^{2}= 36: You can express this equation as 1*x*^{2}+ 0*x*+ (–36) = 0. So*a*= 1,*b*= 0, and*c*= –36.- 3
*x*^{2}+ 6*x*+ 4 = –33: Expressed in quadratic form, this equation reads 3*x*^{2}+ 6*x*+ 37 = 0. So*a*= 3,*b*= 6, and*c*= 37.

Solve: *x*^{2} + 5*x* + 6 = 0.

The equation is already expressed in quadratic form here (the expression on the left is equal to zero), saving you a little time.

You can use the factoring method for most quadratic equations where a = 1 and c is a positive number.

The first step in factoring a quadratic equation is to draw two sets of parentheses on your scratch paper, and then place an*x*at the front of each, leaving some extra space after it. As with the original quadratic, the equation should equal zero: (

*x*)(

*x*) = 0.

The next step is to find two numbers that equal *c* when multiplied together and equal *b* when added together. In the example equation, *b* = 5 and *c* = 6, so you need to hunt for two numbers that multiply to 6 and add up to 5. For example,

and 2 + 3 = 5. In this case, the two numbers you're seeking are positive 2 and positive 3.

Finally, put these two numbers into your set of parentheses:

(*x* + 2)(*x* + 3) = 0 Any number multiplied by zero equals zero, which means that *x* + 2 = 0 and/or *x* + 3 = 0. The solution to this quadratic equation is *x* = –2 and/or *x* = –3.