Solve the equation x^{2}-2x-15 = 0
The general format for an equation of this type is ax2+bx+c Firstly you should factor the equation. Since in the example given a=1 you know that there will be a single x term in each factor. So you have (x+ unknown) (x+unknown) = 0Next, the c term should be factored. 15 can be factored as 1x15, or 3x5. Once you have the potential factors, you need to see if it is possible to add or subtract the individual terms to equal b. So in this case b=-2 and it is possible by using the 3x5 factor (3-5 = -2)Once you have all the numbers you can write out the final factor as (x-5)(x+3) = 0 note make sure to watch the negative signs hereYou can check that you are correct up to this point by expanding the factors so (x-5)(x+3) = x2 -5x +3x -15 = x2-2x-15 = 0Once you have factored the equation you must then set each individual factor equal to zero and solve.So (x-5) = 0, x=5and (x+3) = 0, x=-3Thus the two solutions to the equation are x=-3 and x=5.note, if this problem is a word problem that has been put into context you must check that both answers make sense. If it is asking you for a quantity of objects for example, the negative answer does not make sense so the only realistic answer would be 5
