SOLUTION: -20-3x+3x^2=0 I know that the trinomial cannot be factored, but is there another way to solve the equation?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: -20-3x+3x^2=0 I know that the trinomial cannot be factored, but is there another way to solve the equation?      Log On


   

Question 153341: -20-3x+3x^2=0
I know that the trinomial cannot be factored, but is there another way to solve the equation?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Yes there is!
Quadratic equations can always be solved by 1) completing the square: and 2) using the quadratic formula.
Solve for x:
-20-3x%2B3x%5E2+=+0 Rearrange this so that it is in standard form:
3x%5E2-3x-20+=+0 Apply the quadratic formula: x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
The a, b, and c come from the general form of the quadratic equation: ax%5E2%2Bbx%2Bc+=+0, so in this case, a = 3, b = -3, and c = -20.
Making the appropriate substitutions, we get:
x+=+%28-%28-3%29%2B-sqrt%28%28-3%29%5E2-4%283%29%28-20%29%29%29%2F2%283%29 Simplifying this, we get:
x+=+%283%2B-sqrt%289-%28-240%29%29%29%2F2%283%29
x+=+%283%2B-sqrt%28249%29%29%2F6
x+=+%283%2Bsqrt%28249%29%29%2F6 or x+=+%283-sqrt%28249%29%29%2F6 These are the exact solutions. For the approximate numeric solutions, take the square roots where indicated:
x+=+%283%2B15.8%29%2F6 or x+=+%283-15.8%29%2F6
x+=+3.13 or x+=+-2.13