SOLUTION: please help me solve this problem {{{x^2-2x-4=0}}}

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Question 33711: please help me solve this problem
x%5E2-2x-4=0
Answer by ntnk(54) 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 1x%5E2%2B-2x%2B-4+=+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=%28-2%29%5E2-4%2A1%2A-4=20.

Discriminant d=20 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+20+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+3.23606797749979
x%5B2%5D+=+%28-%28-2%29-sqrt%28+20+%29%29%2F2%5C1+=+-1.23606797749979

Quadratic expression 1x%5E2%2B-2x%2B-4 can be factored:
1x%5E2%2B-2x%2B-4+=+1%28x-3.23606797749979%29%2A%28x--1.23606797749979%29
Again, the answer is: 3.23606797749979, -1.23606797749979. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-4+%29


Also, if you go back to where the equation was plugged into the quadratic equation:
%28-%28-2%29+%2B-+sqrt%2820%29%29%2F%282%2A1%29
It can be simplified to:
%282+%2B-+2%2Asqrt%285%29%29%2F2
And further simplified to
1+%2B-+sqrt%285%29 by canceling the 2's
NtNk