SOLUTION: Solve the following quadratic equations by factoring or by any of the techniques of this chapter. Explain why you chose one method over the other for each problem. {{{x^2-9x-4=6

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the following quadratic equations by factoring or by any of the techniques of this chapter. Explain why you chose one method over the other for each problem. {{{x^2-9x-4=6      Log On


   

Question 74853This question is from textbook Beginning Algebra
: Solve the following quadratic equations by factoring or by any of the techniques of this chapter. Explain why you chose one method over the other for each problem.
x%5E2-9x-4=6
The answer I got for this one is
x%5E2-9%2Ax-4=6
%28x%5E2-9%2Ax-4%29%2B%28-6%29=6%2B%28-6%29
x%5E2-9%2Ax-4-6=6-6
x%5E2-9%2Ax-10=0
x=%28-%28-9%29%2B2sqrt%28-9%29%5E2-4%2A1%2A%28-10%29%29%2F%282%2A1%29,x=%28-%28-9%29-2sqrt%28-9%29%5E2-4%2A1%2A%28-10%29%29%2F%282%2A1%29
x=%28-%28-9%29%2B2sqrt%28-9%29%5E2-4%2A1%2A%28-10%29%29%2F2,x=%28-%28-9%29-2sqrt%28-9%29%5E2-4%2A1%2A%28-10%29%29%2F2
x=%28-%28-9%29%2B2sqrt%28%28-%283%5E2%29%29%5E2-4%2A%28-10%29%29%29%2F2,x=%28-%28-9%29-2sqrt%28%28-%283%5E2%29%29%5E2-4%2A%28-10%29%29%29%2F2
x=%28-%28-9%29%2B2sqrt%28%28-9%29%5E2-4%2A%28-10%29%29%29%2F2,x=%28-%28-9%29-2sqrt%28%28-9%29%5E2-4%2A%28-10%29%29%29%2F2
x=%28-%28-9%29%2B2sqrt%28%283%5E2%29%5E2%2B40%29%29%2F2,x=%28-%28-9%29-2sqrt%28%283%5E2%29%5E2%2B40%29%29%2F2
x=%28-%28-9%29%2B2sqrt%289%5E2%2B40%29%29%2F2,x=%28-%28-9%29-2sqrt%289%5E2%2B40%29%29%2F2
x=%28-%28-9%29%2B2sqrt%28%283%5E2%29%5E2%2B40%29%29%2F2,x=%28-%28-9%29-2sqrt%28%283%5E2%29%5E2%2B40%29%29%2F2
x=%28-%28-9%29%2B2sqrt%289%5E2%2B40%29%29%2F2,x=%28-%28-9%29-2sqrt%289%5E2%2B40%29%29%2F2
x=%28-%28-9%29%2B2sqrt%28%283%5E2%29%5E2%2B40%29%29%2F2,x=%28-%28-9%29-2sqrt%28%283%5E2%29%5E2%2B40%29%29%2F2
x=%28-%28-9%29%2B2sqrt%283%5E%282%2A2%29%2B40%29%29%2F2,x=%28-%28-9%29-2sqrt%283%5E%282%2A2%29%2B40%29%29%2F2
x=%28-%28-9%29%2B2sqrt%283%5E4%2B40%29%29%2F2,x=%28-%28-9%29-%283%5E4%2B40%29%29%2F2
x=%28-%28-9%29%2B2sqrt%2881%2B40%29%29%2F2,x=%28-%28-9%29-2sqrt%2881%2B40%29%29%2F2
x=%28-%28-9%29%2B2sqrt%28121%29%29%2F2,x=%28-%28-9%29-2sqrt%28121%29%29%2F2
x=%28-%28-9%29%2B2sqrt%2811%5E2%29%29%2F2,x=%28-%28-9%29-2sqrt%2811%5E2%29%29%2F2
:
x=%28-%28-9%29%2B%282%2F2%29sqrt%2811%5E%282%2F2%29%29%29%2F2,x=%28-%28-9%29-%282%2F2%29sqrt%2811%5E%282%2F2%29%29%29%2F2
x=%28-%28-9%29%2B%281%2F1%29sqrt%2811%5E%281%2F1%29%29%29%2F2,x=%28-%28-9%29-%281%2F1%29sqrt%2811%5E%281%2F1%29%29%29%2F2
x=%28-%28-9%29%2B1sqrt%2811%5E1%29%29%2F2,x=%28-%28-9%29-1sqrt%2811%5E1%29%29%2F2
x=%28-%28-9%29%2B1sqrt%2811%29%29%2F2,x=%28-%28-9%29-1sqrt%2811%29%29%2F2
x=%28-%28-9%29%2B11%29%2F2,x=%28-%28-9%29-11%29%2F2
x=%289%2B11%29%2F2,x=%289-11%29%2F2
x=20%2F2,x=%28-2%29%2F2
x=2%5E2%2A5%2F2,x=%28-2%29%2F2
x=2%5E%282-1%29%2A5%2F1,x=%28-2%29%2F2
x=2%5E1%2A5%2F1,x=%28-2%29%2F2
x=2%2A5%2F1,x=%28-2%29%2F2
x=2%2A5,x=%28-2%29%2F2
x=10,x=%28-2%29%2F2
x=10,x=-1%2F1
x=10,x=-1
Is this correct. I am not sure which method I used and why I would use this particular method over another and need some help with that.Thanks (Sorry this is so long I don't like to do this because of that, but I wanted you to see my work on this one.) This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You've got it. Not the route I would take, but it gets you to the answer nonetheless. I would've factored the left side to easily solve for x.

x%5E2-9%2Ax-10=0 What 2 numbers multiply to -10 and add to -9. They are -10 and 1
%28x%2B1%29%28x-10%29=0Factor the left side
x%2B1=0Set each factor equal to 0
x=-1There's one answer
x-10=0
x=10There's the other answer
So x=-1 or x=10
But if it works for you then you should stick with it.