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Solving for the Quadratic Formula

Module by: Brian West. E-mail the author

a⁢x2+b⁢x+c=0 x2+ba⁢x+ca=0 x2+ba⁢x=−ca x2+ba⁢x+b2⁢a2=b2⁢a2−ca x+b2⁢a2=b2⁢a2−ca x+b2⁢a2=b24⁢a2−ca x+b2⁢a2=b24⁢a2−4⁢a4⁢a⁢ca x+b2⁢a2=b24⁢a2−4⁢a⁢c4⁢a2 x+b2⁢a2=b2−4⁢a⁢c4⁢a2 x+b2⁢a= ± ⁢b2−4⁢a⁢c4⁢a2 x+b2⁢a= ± ⁢b2−4⁢a⁢c4⁢a2 x+b2⁢a= ± ⁢b2−4⁢a⁢c2⁢a x= ± ⁢b2−4⁢a⁢c2⁢a−b2⁢a x= ± ⁢−bb2−4⁢a⁢c2⁢a a x 2 b x c 0 x 2 b a x c a 0 x 2 b a x c a x 2 b a x b 2 a 2 b 2 a 2 c a x b 2 a 2 b 2 a 2 c a x b 2 a 2 b 2 4 a 2 c a x b 2 a 2 b 2 4 a 2 4 a 4 a c a x b 2 a 2 b 2 4 a 2 4 a c 4 a 2 x b 2 a 2 b 2 4 a c 4 a 2 x b 2 a ± b 2 4 a c 4 a 2 x b 2 a ± b 2 4 a c 4 a 2 x b 2 a ± b 2 4 a c 2 a x ± b 2 4 a c 2 a b 2 a x ± b b 2 4 a c 2 a
(1)

which is usually seen as

x=-b±b2-4ac2ax=-b±b2-4ac2a
(2)

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