Quadratic Equation Formula

Quadratic Equation Formula and factoring from the Standard Equation top left imageQuadratic Equation Formula and factoring from the Standard Equation top right image
HomeAlgebraQuadratic Equation

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.

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

ax2 + bx = - c

Divide both sides of equation by ”a”.

           b             -c

x2  +  —  x  =     —

           a              a

Complete the trinomial square.

           b

x2  +  —  x

           a

+

(

 b

2a

 2

)

=

  -c

  —

   a

+

(

  b

 —

 2a

)

 2

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.

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