SOLUTION: Please help. My worksheet says: Find the exact solutions to 6x^2+x+4=0 by using the Quadratic Formula. Thanks

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Please help. My worksheet says: Find the exact solutions to 6x^2+x+4=0 by using the Quadratic Formula. Thanks      Log On


   

Question 161413: Please help. My worksheet says: Find the exact solutions to 6x^2+x+4=0 by using the Quadratic Formula.
Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6x%5E2%2Bx%2B4=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=6, b=1, and c=4


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-%281%29+%2B-+sqrt%28+%281%29%5E2-4%286%29%284%29+%29%29%2F%282%286%29%29 Plug in a=6, b=1, and c=4


x+=+%28-1+%2B-+sqrt%28+1-4%286%29%284%29+%29%29%2F%282%286%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1-96+%29%29%2F%282%286%29%29 Multiply 4%286%29%284%29 to get 96


x+=+%28-1+%2B-+sqrt%28+-95+%29%29%2F%282%286%29%29 Subtract 96 from 1 to get -95


x+=+%28-1+%2B-+sqrt%28+-95+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%28-1+%2B-+i%2Asqrt%2895%29%29%2F%2812%29 Simplify the square root


x+=+%28-1%2Bi%2Asqrt%2895%29%29%2F%2812%29 or x+=+%28-1-i%2Asqrt%2895%29%29%2F%2812%29 Break up the expression.


So the answers are x+=+%28-1%2Bi%2Asqrt%2895%29%29%2F%2812%29 or x+=+%28-1-i%2Asqrt%2895%29%29%2F%2812%29