Quadratic Equations

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What is a Quadratic Equation? A quadratic equation is a single-variable equation in which the highest power on the variable is 2. The standard form is:
a x 2 + b x + c = 0
where a , b , and c are real numbers and a 0 .
 
Solving Quadratic Equations There are three methods for solving a quadratic equations:
Factoring
Factoring is a process of changing the form of an equation from the standard form into the product of two factors:
( a x + b ) ( c x + d ) = 0
Once the equation is in this form, each factor is set equal to 0 and solved for x. This uses the Zero-Product Property that says if the product of two factors equals zero, then at least one of the factors must equal zero.
( a x + b ) = 0 OR ( c x + d ) = 0
Completing the Square
Completing the square is a process of changing the form of an equation from the standard form so that both sides are perfect squares:
( x + b ) 2 = c 2
Once it’s in this form, the solutions can be found by taking the square root of both sides and solving for x.

Quadratic Formula
The quadratic formula is:
x = - b ± b 2 - 4 a c 2 a
I prefer this form:
x = - b ± d 2 a where d is the discriminant b 2 - 4 a c
 
Solve a Quadratic Equation
Enter values for:     Choose your method(s):     Solve it!
a   b   c      


   
x 2 + x + = 0
 

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