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X  =   —––––––––––––

− b ± √(b2 − 4ac)

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”.

X =

− b ± √(b2 − 4ac )

____________

2a