SOLUTION: 0.6x^2=1.2x+0.6

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Question 436577: 0.6x^2=1.2x+0.6
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
0.6x^2=1.2x+0.6
multiply by 10 to rid ourselves of decimal points:
6x^2=12x+6
divide both sides by 6:
x^2=2x+1
move everything to the left:
x^2-2x-1=0
can't factor so apply the quadratic formula to get:
x = {2.41, -0.41}
.
details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-1+=+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-1=8.

Discriminant d=8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+8+%29%29%2F2%5C1+=+2.41421356237309
x%5B2%5D+=+%28-%28-2%29-sqrt%28+8+%29%29%2F2%5C1+=+-0.414213562373095

Quadratic expression 1x%5E2%2B-2x%2B-1 can be factored:
1x%5E2%2B-2x%2B-1+=+1%28x-2.41421356237309%29%2A%28x--0.414213562373095%29
Again, the answer is: 2.41421356237309, -0.414213562373095. 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-1+%29