SOLUTION: I need steps and solution to this equation: 1/18h² - 1/2h + 1 = 0 Thanks

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Question 43873: I need steps and solution to this equation:
1/18h² - 1/2h + 1 = 0


Thanks
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ah%5E2%2Bbh%2Bc=0 (in our case 0.0555555555555556h%5E2%2B-0.5h%2B1+=+0) has the following solutons:

h%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=%28-0.5%29%5E2-4%2A0.0555555555555556%2A1=0.0277777777777776.

Discriminant d=0.0277777777777776 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--0.5%2B-sqrt%28+0.0277777777777776+%29%29%2F2%5Ca.

h%5B1%5D+=+%28-%28-0.5%29%2Bsqrt%28+0.0277777777777776+%29%29%2F2%5C0.0555555555555556+=+5.99999999999999
h%5B2%5D+=+%28-%28-0.5%29-sqrt%28+0.0277777777777776+%29%29%2F2%5C0.0555555555555556+=+3

Quadratic expression 0.0555555555555556h%5E2%2B-0.5h%2B1 can be factored:
0.0555555555555556h%5E2%2B-0.5h%2B1+=+0.0555555555555556%28h-5.99999999999999%29%2A%28h-3%29
Again, the answer is: 5.99999999999999, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.0555555555555556%2Ax%5E2%2B-0.5%2Ax%2B1+%29



The 5.999999999 is probably just a rounding error, caused by the neverending expansion of 1%2F18. You can consider it as 6.