SOLUTION: I cannot figure out this quadratic eqation: x^2 + x =0

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Question 297637: I cannot figure out this quadratic eqation: x^2 + x =0
Found 2 solutions by nyc_function, richwmiller:
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + x = 0
Factor the left side.
x(x + 1) = 0
Set each factor to zero.
x = 0
or
x + 1 = 0
x = -1
Answers: x = 0 and x = -1

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
There are several ways to do this.
factor
x*(x+1)=0
x=0
x=-1
(x=0,-1)
complete the square
x^2+x+ (1/2)^2=1/4
(x+1/2)^2=1/4
x+1/2=1/2
x=0
x+1/2=-1/2
x=-1
x=(0,-1)
quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B0+=+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=%281%29%5E2-4%2A1%2A0=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+0
x%5B2%5D+=+%28-%281%29-sqrt%28+1+%29%29%2F2%5C1+=+-1

Quadratic expression 1x%5E2%2B1x%2B0 can be factored:
1x%5E2%2B1x%2B0+=+1%28x-0%29%2A%28x--1%29
Again, the answer is: 0, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B0+%29