Show that the transformation x = z −"\\frac{b}{3a}" converts the cubic equation ax3 + bx2 + cx + d= 0 into one of the form z3 + 3Hz + G = 0, i.e. the x2 term goes away.
"x^2=z^2-\\dfrac{2bz}{3a}+\\dfrac{b^2}{9a^2}"
"x^3=z^3-\\dfrac{bz^2}{a}+\\dfrac{b^2z}{3a^2}-\\dfrac{b^3}{27a^3}"
Substitute
"+bz^2-\\dfrac{2b^2z}{3a}+\\dfrac{b^3}{9a^2}"
"cz-\\dfrac{bc}{3a}+d=0"
"az^3+(-\\dfrac{b^2}{3a}+c)z+(\\dfrac{2b^3}{9a^2}-\\dfrac{bc}{3a}+d)=0"
"z^3+3(-\\dfrac{b^2}{3a^2}+\\dfrac{c}{3a})z+(\\dfrac{2b^3}{9a^3}-\\dfrac{bc}{3a^2}+\\dfrac{d}{a})=0"
"H=-\\dfrac{b^2}{3a^2}+\\dfrac{c}{3a}"
"G=\\dfrac{2b^3}{9a^3}-\\dfrac{bc}{3a^2}+\\dfrac{d}{a}"
"z^3+3Hz+G=0"
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