SOLUTION: The problem is x(squared)-(minus)x-(minus)6 I figured out the solutions (x= -2, 3) by solving by factoring but when I try and do it by solving by the quadratic formula, I keep g

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The problem is x(squared)-(minus)x-(minus)6 I figured out the solutions (x= -2, 3) by solving by factoring but when I try and do it by solving by the quadratic formula, I keep g      Log On


   

Question 380056: The problem is x(squared)-(minus)x-(minus)6
I figured out the solutions (x= -2, 3) by solving by factoring but when I try and do it by solving by the quadratic formula, I keep getting stuck. Can you please explain the steps to solve the problem using the quadratic formaula?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-x-6=0 Start with the given equation.


Notice that the quadratic x%5E2-x-6 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-1, and C=-6


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-6%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-1, and C=-6


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-6%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%28-6%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--24+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-6%29 to get -24


x+=+%281+%2B-+sqrt%28+1%2B24+%29%29%2F%282%281%29%29 Rewrite sqrt%281--24%29 as sqrt%281%2B24%29


x+=+%281+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29 Add 1 to 24 to get 25


x+=+%281+%2B-+sqrt%28+25+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+5%29%2F%282%29 Take the square root of 25 to get 5.


x+=+%281+%2B+5%29%2F%282%29 or x+=+%281+-+5%29%2F%282%29 Break up the expression.


x+=+%286%29%2F%282%29 or x+=++%28-4%29%2F%282%29 Combine like terms.


x+=+3 or x+=+-2 Simplify.


So the solutions are x+=+3 or x+=+-2

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim