SOLUTION: Please solve this for me! 3x^2+x+4

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please solve this for me! 3x^2+x+4      Log On


   

Question 883291: Please solve this for me! 3x^2+x+4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to solve 3x%5E2%2Bx%2B4=0




3x%5E2%2Bx%2B4=0 Start with the given equation.


Notice that the quadratic 3x%5E2%2Bx%2B4 is in the form of Ax%5E2%2BBx%2BC where A=3, 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%283%29%284%29+%29%29%2F%282%283%29%29 Plug in A=3, B=1, and C=4


x+=+%28-1+%2B-+sqrt%28+1-4%283%29%284%29+%29%29%2F%282%283%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1-48+%29%29%2F%282%283%29%29 Multiply 4%283%29%284%29 to get 48


x+=+%28-1+%2B-+sqrt%28+-47+%29%29%2F%282%283%29%29 Subtract 48 from 1 to get -47


x+=+%28-1+%2B-+sqrt%28+-47+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-1+%2B-+i%2Asqrt%2847%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-1%2Bi%2Asqrt%2847%29%29%2F%286%29 or x+=+%28-1-i%2Asqrt%2847%29%29%2F%286%29 Break up the expression.


So the solutions are x+=+%28-1%2Bi%2Asqrt%2847%29%29%2F%286%29 or x+=+%28-1-i%2Asqrt%2847%29%29%2F%286%29


Note: i+=+sqrt%28-1%29

If you have not learned about complex numbers yet, then you can say "there are no real solutions"