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Algebra

Factorization of Quadratic Equation

The solution of a quadratic equation   ax2 + bx + c = 0   is given by:

x    =  
b ± √ b2 – 4ac
2a

This is derived as follows: We have

ax2 + bx + c    =   0

dividing through by a:

x2 +
b
a
x
c
a
   =   0

 factorizing:

  x  +
b
2a
 
2
 
 – 
b2
4a2
 +
c
a
   =   0

 so

  x  +
b
2a
 
2
 
 =
b2 – 4ac
4a2

taking square roots of both sides

x  +
b
2a
   =
±√ b2 – 4ac
2a

and hence the result.