SOLUTION: Must solve using the quadratic formula: {{{sqrt(5)x^2 + 2x + 1 = 0}}}. So far, I have gotten {{{(-2+-sqrt(4-4sqrt(5)))/(2sqrt(5))}}}, but I don't know how to simplify it further.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Must solve using the quadratic formula: {{{sqrt(5)x^2 + 2x + 1 = 0}}}. So far, I have gotten {{{(-2+-sqrt(4-4sqrt(5)))/(2sqrt(5))}}}, but I don't know how to simplify it further.      Log On


   

Question 892926: Must solve using the quadratic formula: sqrt%285%29x%5E2+%2B+2x+%2B+1+=+0. So far, I have gotten %28-2%2B-sqrt%284-4sqrt%285%29%29%29%2F%282sqrt%285%29%29, but I don't know how to simplify it further.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2.23606797749979x%5E2%2B2x%2B1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A2.23606797749979%2A1=-4.94427190999916.

The discriminant -4.94427190999916 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -4.94427190999916 is + or - sqrt%28+4.94427190999916%29+=+2.22357188100568.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2.23606797749979%2Ax%5E2%2B2%2Ax%2B1+%29