[hvyhgffd] The golden ratio and the square root of 125

phi = (1+sqrt(5))/2 = sqrt(5)/2 + 1/2 = sqrt(5)/sqrt(4) + 1/2 = sqrt(5/4) + 1/2 = sqrt(5*0.25) + 1/2 = sqrt(5*0.25*100*0.01) + 1/2 = sqrt(125*0.01) + 1/2 = sqrt(125)*sqrt(0.01) + 1/2 = sqrt(125)*0.1 + 1/2 = sqrt(125)/10 + 1/2 = sqrt(125)/10 + 5/10 = (sqrt(125) + 5)/10

This is useful for directly calculating the digits of phi in base 10 because it doesn't need the final division by 2 that the original formula requires.

1.618033989 = phi
11.18033989 = sqrt 125

Apply the quadratic formula to 5x^2 - 5x - 5 = 0.