I am doing some homework on the golden ratio, and I'm told that the short side (b) is 10, and I am now trying to calculate side a... I have this so far http://mathbin.net/149853 and should get a when trowing it through the formula for quadratic equation, but what I get for a does not ad up to 0 when calculating what I have shown in the links... I have been staring at this for hours now. Please help :)

Question

anonymous · Answer

the solution of your equation is x=5+5sqrt(5)

anonymous · Answer

Are we looking at the same equation?

$$\frac{a+10}{a}=\frac{a}{10}\leftrightarrow a+10=\frac{a^{2}}{10}\leftrightarrow 10a+10^{2}=a^{2}\leftrightarrow -a^{2}+10a+10^{2}=0$$

anonymous · Answer

yes a is equal to 5+5*sqrt(5)

anonymous · Answer

That does not make any sense to me (:

my problem is that if I made this equation right then

$$a=\frac{-10\pm \sqrt{10^{2}-4*-1*10^{2}}}{2*10}$$

And when I do that calculation I don't get a number that adds up to 0 in

$$-a^{2}+10a+10^{2}=0$$

anonymous · Answer

hm where did you get this equation for a?
the equation is (-10-sqrt(10^2-4*-1*10^2))/-2
why do you divide by 2*10? the coefficient before a^2 is -1 not 10
you should divide by 2*coeffiecient of x^2,so it's -2, not 20

anonymous · Answer

I got it from Khan Academy that it should be:
(-b+-sqrt(b^2-4ac))/2a
so yes you are right that I made a mistake in the last part, it's solved now THANK YOU :D