+386 Hi there!
Just learned the "completing the square" method (sorry that might be a litteral translation from french but eh didn't find anything better...).
I'm now stuck with this exercise because this one in particular, instead of being in the usual form ax^2 + bx + c =0, it has an additionnal vari:
5ax^2 - 10ax + 7 = 0 (where a isn't equal to 0 )
Need to find the roots!
I know of the usual b^2-4ac to right away know if there is any roots at all, but I really don't know how to deal with the unexpected "a"s they added in there...
Thanks in advance!
+33653 "completing the square" is the correct term in English.
5ax2 - 10ax + 7 = 0
Divide through by 5a
x2 - 2x + 7/(5a) = 0
Add 1 to both sides:
x2 - 2x + 1 + 7/(5a) = 1
(x - 1)2 +7/(5a) = 1
Subtract 7/(5a) from both sides
(x - 1)2 = 1 - 7/(5a)
x - 1 = sqrt(1 - 7/(5a)) and x - 1 = -sqrt(1 - 7/(5a))
x = 1 + sqrt(1 - 7/(5a)) and x = 1 - sqrt(1 - 7/(5a))
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