SOLUTION: Solve by quadratic formula and simplify {{{7x^2 -x-6=0}}} Do I just factor this problem now since it is already in standard form? I am not sure

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve by quadratic formula and simplify {{{7x^2 -x-6=0}}} Do I just factor this problem now since it is already in standard form? I am not sure      Log On


   

Question 264648: Solve by quadratic formula and simplify
7x%5E2+-x-6=0
Do I just factor this problem now since it is already in standard form? I am not sure
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

7x%5E2-x-6=0 Start with the given equation.


Notice that the quadratic 7x%5E2-x-6 is in the form of Ax%5E2%2BBx%2BC where A=7, 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%287%29%28-6%29+%29%29%2F%282%287%29%29 Plug in A=7, B=-1, and C=-6


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%287%29%28-6%29+%29%29%2F%282%287%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%287%29%28-6%29+%29%29%2F%282%287%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--168+%29%29%2F%282%287%29%29 Multiply 4%287%29%28-6%29 to get -168


x+=+%281+%2B-+sqrt%28+1%2B168+%29%29%2F%282%287%29%29 Rewrite sqrt%281--168%29 as sqrt%281%2B168%29


x+=+%281+%2B-+sqrt%28+169+%29%29%2F%282%287%29%29 Add 1 to 168 to get 169


x+=+%281+%2B-+sqrt%28+169+%29%29%2F%2814%29 Multiply 2 and 7 to get 14.


x+=+%281+%2B-+13%29%2F%2814%29 Take the square root of 169 to get 13.


x+=+%281+%2B+13%29%2F%2814%29 or x+=+%281+-+13%29%2F%2814%29 Break up the expression.


x+=+%2814%29%2F%2814%29 or x+=++%28-12%29%2F%2814%29 Combine like terms.


x+=+1 or x+=+-6%2F7 Simplify.


So the solutions are x+=+1 or x+=+-6%2F7