Solve: x^2 – x – 12 = 0

Method 1: Solve by inspection.
Demonstrate that quadratic equations can often be written in the form (x+a)(a+b) = 0. Explain that possible solutions arise as a result of either (x+a) or (x+b) =0. Note that ab = -12 , and a+b = -1 (the coefficient of the x term). Through solving these simultaneous equations or simple inspection we conclude that:a = -4, b = +3. We then substitute these values into our original form: (x+a)(a+b) = 0 , concluding that x must equal 4, -3.
Method 2: Use the quadratic formula (-b+-(√b^2-4ac) ) / 2a.
Substituting a = 1, b = -1, c= -12 we arrive at the answer x = 4,-3.