Top of Page
Home Algebra Quadratic Equation

Quadratic Equation Formula

The Quadratic Equation Formula is:

- b ± √(b2 - 4ac)

X  =   —––––––––––––

2a

A quadratic can be solved for x when the values for a, b and c of the Standard Equation, ax2 + bx + c, are known. The Quadratic Formula is factored from the Standard Equation by Completing the Square.

ax2 + bx = - c

Place constant of Standard Equation to the right side of equals sign.

            b              -c

x2  +  —  x  =     —

            a               a

Divide both sides of equation by ”a”.

            b

x2  +  —  x

            a

+

(

 b

2a

 2

)

=

  -c

  —

   a

+

(

  b

 —

 2a

)

 2

Complete the trinomial square.

Simplify equation terms step 1.

(

         b

x +  —–

         2a

)

 2

=

  -c

  —

   a

 4a  —  4a

+

  b2  —–   4a2

Simplify equation terms step 2.

(

         b

x +  —–

         2a

)

 2

=

b2 - 4ac

 —––––

     4a2

Square root  both sides of equation.

(

         b

x +  —–

         2a

)

=

b2 - 4ac

 —––––

     4a2

Simplify equation terms.

         b

x +  —–

         2a

=

±

√(b2 - 4ac )

  —––––––

    √(4a2 )

Simplify equation terms.

         b

x +  —–

         2a

=

±

√(b2 - 4ac )

  —––––––

        2a

Solve for “x”.

- b ± √(b2 - 4ac )

  ____________

             2a

X =

The Quadratic Equation Formula.

Copyright © DigitMath.com

All Rights Reserved.

About Privacy