 then x2 - 5x + 6 = 12. Subtract 12 from both sides of the equation SO that we set the left hand side equal to 0. Thus: x2 - 5x - 6 = 0 factors into (x - 6)(x + = 0. X - 6 0, or + = 0, x = -1. Quadratic Formula. This formula may be used on the conventional quadratic equation in the generic form of Ax2 C = 0 (A # 0). X is solved by simply manipulating the constants A, B, and C. The quadratic formula is stated as follows: X = [-B(B2-4AC)1/2/2A - or, rewritten with the radical sign: Just like we did with the factoring method, the quadratic formula will produce two roots (two answers): one with the plus before the radical sign and one with the minus before the radical sign. A REVIEW OF MATHEMATICS FOR TELECOMMUNICATION APPLICATIONS Example 1: Solve for X: 3x2 - 2x - 5 = 0. Here A = 3, B = -2, and C = -5. Apply the quadratic formula. X = (+2 + 4 + 60)/6. The first possibility is (+2 +64)/6 = 10/6; the second possibility is (+2 - 8)/6 = -1. The quadratic formula will not handle the square root of a negative number. The square root of a negative number can usually be factored down to (-1)1/2, , which, by definition, is the imaginary number i, and is beyond the scope of this appendix. Example 2: Solve for E: E2 - 3E - 2 = 0. A = 1, B = -3, and C = -2. Thus E = (+3 +9 + 8)/2. The first possibility is (3 + 4.123)/2 and the second possibility is (3 - 4.123)/2. Thus E = 3.562 or -0.562. B.3.5 Solving Two Simultaneous Linear Equations with Two Unknowns There are two methods of solving two simultaneous equations: 1. The graphical method where both equations are plotted and the intersection of the line derived is the common solution. 2. The algebraic solution. We will concentrate on the algebraic solution. There are two approaches to solving two simultaneous equations by the algebraic solution: A. Elimination B. Substitution The Elimination Method. With this method we manipulate one of the equations such that when the two equations are either added or subtracted, one of the unknowns is eliminated. We then solve for the other un