You can help keep this site free, by visiting our sponsor, Algebrator - an incredible software program that provides step - by - step solution to not only equations but to any other algebra problem as well!
home
solving equations with fractions
methods for solving quadratic equations
solving equations
solving equations
linear equations
solving equations
solving equations with variables on each side
solving equations
linear equations
solving linear equations
steps for solving linear equations
solving equations with variables on each side
solving quadratic equations
solving equations
solving equations
steps for solving linear equations
quadratic equations
writing linear equations
solving equations
solving rational equations
solving equations
solving equations
solving systems of equations using elimination
solving linear equations
solving equations
solving quadratic equations
methods for solving quadratic equations
solving equations
solving equations
equation solving resources
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Quadratic equations are of the form ax + bx + c = 0, where a 0

Quadratics may have two, one, or zero real solutions .

1. Completing the Square

If the quadratic equation is of the form ax + bx + c = 0, where a 0 and the quadratic expression is not factorable, try completing the square.

Example: x + 6x - 11 = 0

**Important: If a 1, divide all terms by “a” before proceeding to the next steps.

Move the constant to the right side x + 6x = 11
Find half of b, which means
Find : 3 = 9
Add to both sides of the equation x + 6x + 9 = 11 + 9
Factor the quadratic side (x + 3)(x + 3) = 20
(which is a perfect square because you just made it that way!)
Then write in perfect square form (x + 3)= 20
Take the square root of both sides
Solve for x Simplify the radical

  This represents the exact answer.

Decimal approximations can be found using a calculator.

 

2. Quadratic Formula

Any quadratic equation of the form ax + bx + c = 0, where a 0 can be solved for both real and imaginary solutions using the quadratic formula:

Example: x + 6x - 11 = 0 (a = 1, b = 6, c = -11)

Substitute values into the quadratic formula:

Simplify the radical

This is the final simplified EXACT answer.