SOLUTION: I am stumped on this problem. 3x^2-x-1=0. I am needing to solve it by either quadratic equation or finding the square root. Has to be completely worked out with all steps.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I am stumped on this problem. 3x^2-x-1=0. I am needing to solve it by either quadratic equation or finding the square root. Has to be completely worked out with all steps.       Log On


   

Question 159309: I am stumped on this problem. 3x^2-x-1=0. I am needing to solve it by either quadratic equation or finding the square root. Has to be completely worked out with all steps.
If anyone could help I would appreciate it. This is the last question on my assignment.
Thank you,
Renee
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2-x-1=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=3, b=-1, and c=-1


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%283%29%28-1%29+%29%29%2F%282%283%29%29 Plug in a=3, b=-1, and c=-1


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%283%29%28-1%29+%29%29%2F%282%283%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%283%29%28-1%29+%29%29%2F%282%283%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--12+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-1%29 to get -12


x+=+%281+%2B-+sqrt%28+1%2B12+%29%29%2F%282%283%29%29 Rewrite sqrt%281--12%29 as sqrt%281%2B12%29


x+=+%281+%2B-+sqrt%28+13+%29%29%2F%282%283%29%29 Add 1 to 12 to get 13


x+=+%281+%2B-+sqrt%28+13+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%281%2Bsqrt%2813%29%29%2F%286%29 or x+=+%281-sqrt%2813%29%29%2F%286%29 Break up the expression.


So the answers are x+=+%281%2Bsqrt%2813%29%29%2F%286%29 or x+=+%281-sqrt%2813%29%29%2F%286%29


which approximate to x=0.768 or x=-0.434