SOLUTION: (.2x-3)^2-1=x

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Question 27645: (.2x-3)^2-1=x
Answer by askmemath(368) About Me  (Show Source):
You can put this solution on YOUR website!
Expanding we get
+4x%5E2+%2B9+-12x+-1+=+x
+4x%5E2+%2B8+-12x++-x=+0
+4x%5E2+%2B8+-13x++=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-13x%2B8+=+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=%28-13%29%5E2-4%2A4%2A8=41.

Discriminant d=41 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+41+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+41+%29%29%2F2%5C4+=+2.42539052967911
x%5B2%5D+=+%28-%28-13%29-sqrt%28+41+%29%29%2F2%5C4+=+0.824609470320894

Quadratic expression 4x%5E2%2B-13x%2B8 can be factored:
4x%5E2%2B-13x%2B8+=+4%28x-2.42539052967911%29%2A%28x-0.824609470320894%29
Again, the answer is: 2.42539052967911, 0.824609470320894. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-13%2Ax%2B8+%29