Dear Ben: Fix the goddamn site please.
A support group for ben to get him to quit putting more "extras" on the site, and just fix the damn thing already.
...hey, Wuss! Can you send that zip file again, but to shamady@ptd.net. For some reason it was downloading, but nothing came through. Could have been something to do with work.
well good to know that your doing well. I remember when you were having so many problems. I was going to help you fix your suburban when you had it, but you got rid of it
x^2 -5x - 16 = 0 Not factorable, use quadratic formula [-b +or- sqrt(b^2 - 4ac)] / 2a where a = 1, b = -5, c = -16 x = {5 + sqrt<[-5]^2 - 4(1)(-16)>} / 2*1 & x = {5 - sqrt<[-5]^2 - 4(1)(-16)>} / 2*1 x = [5 + sqrt(89)]/2 & x = [5 - sqrt(89)]/2 x ~= 7.22 & x ~= -2.22
If the equations are separate: Declare that x =/= -3, -4 Using Fund. Theorem of Algebra, polynomial expansion (12x+19)/[(x+3)(x+4)] = A/(x+3) + B/(x+4), A = (12*-3+19)/(-3+4) = -17, B = (12*-4 + 19)/(-4+3) = 29 (12x+19)/[(x+3)(x+4)] = -17/(x+3) + 29/(x+4) Substituting (12x+19)/[(x+3)(x+4)] for its polynomial expansion 3/(x+3) = -17/(x+3) + 29/(x+4) -5/(x+4) Bringing -17/... to the left, adding 29/... and -5/... together 20/(x+3) = 24/(x+4) Multiplying both sides to clear denoms 20(x+4) = 24(x+3) Solving for x 20x + 80 = 24x + 72 8 = 4x x = 2
2nd equation Declare that x =/= -4, 0 Clear denoms 5x = (x+4)(x-4) Expand and solve for 0 x^2 -5x - 16x = 0 Not factorable, use quadratic formula [-b +or- sqrt(b^2 - 4ac)] / 2a where a = 1, b = -5, c = -16 x = {-5 + sqrt<[-5]^2 - 4(1)(-16)>} / 2*1 & x = {-5 - sqrt<[-5]^2 - 4(1)(-16)>} / 2*1 x = [-5 + sqrt(89)]/2 & x = [-5 - sqrt(89)]/2 x ~= 7.22 & x ~= -2.22
If x has to satisfy both systems, that will be a small nightmare.
