SOLUTION: 4x^2+2x+8=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 4x^2+2x+8=0      Log On


   

Question 187428: 4x^2+2x+8=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2%2B2x%2B8=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=2, and c=8


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-%282%29+%2B-+sqrt%28+%282%29%5E2-4%284%29%288%29+%29%29%2F%282%284%29%29 Plug in a=4, b=2, and c=8


x+=+%28-2+%2B-+sqrt%28+4-4%284%29%288%29+%29%29%2F%282%284%29%29 Square 2 to get 4.


x+=+%28-2+%2B-+sqrt%28+4-128+%29%29%2F%282%284%29%29 Multiply 4%284%29%288%29 to get 128


x+=+%28-2+%2B-+sqrt%28+-124+%29%29%2F%282%284%29%29 Subtract 128 from 4 to get -124


x+=+%28-2+%2B-+sqrt%28+-124+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-2+%2B-+2i%2Asqrt%2831%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-2%2B2i%2Asqrt%2831%29%29%2F%288%29 or x+=+%28-2-2i%2Asqrt%2831%29%29%2F%288%29 Break up the expression.


x+=+%28-1%2Bi%2Asqrt%2831%29%29%2F%284%29 or x+=+%28-1-i%2Asqrt%2831%29%29%2F%284%29 Reduce.



So the answers are x+=+%28-1%2Bi%2Asqrt%2831%29%29%2F%284%29 or x+=+%28-1-i%2Asqrt%2831%29%29%2F%284%29