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# Solving for the Quadratic Formula

Module by: Brian West. E-mail the author

ax2+bx+c=0 x2+bax+ca=0 x2+bax=ca x2+bax+b2a2=b2a2ca x+b2a2=b2a2ca x+b2a2=b24a2ca x+b2a2=b24a24a4aca x+b2a2=b24a24ac4a2 x+b2a2=b24ac4a2 x+b2a= ± b24ac4a2 x+b2a= ± b24ac4a2 x+b2a= ± b24ac2a x= ± b24ac2ab2a x= ± bb24ac2a 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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