As long as x isn't = 0 (and it's not) we have a solution (or two)
First, multiply through by x
This gives us
x^2 +109.9 = 6.7x
Rearranging, we have
x^2 - 6.7x + 109.9 = 0
Let's multiply everything by 10 to get rid of those pesky decimals!!
This gives us
10x^2 - 67x + 1099 = 0
This might factor, but somehow, I doubt it!!
I can tell that we have - possibly - either two positive solutions or zero positive solutions. Further, there are no negative solutions. (If you take pre-calculus, you'll find out why this is true!!)
I see something else, too. If i square (-67), I get 4489. If I multiply the last term, times the first term, times (-4), I get (1099)*(10)*(-4) = -43960. Adding this to 4489 gives me -39471, and this would be the term under the radical in the quad formula. Therefore, since we will get a negative quantity under a square root, we don't have a real number solution.
Just for the heck of it, let's see what the quad formula would produce!!
10x^2 - 67x + 1099 = 0
Yep...just as we expected.......no real solutions!!!
This just proves that a little analysis sometimes is more important than worrying about the "right" answer!!
Hope this helped you!!
