Free Algebra
Tutorials!
 
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.


Solving Quadratic Equations by Completing the Square

Example

Solve by completing the square: 3x2 - 30 = -21x

Solution

Step 1 Isolate the x2-term and the x-term on one side of the equation.

Add 21x to both sides.

Add 30 to both sides.

 3x2 - 30 = -21x

3x2 + 21x - 30 = 0

3x2 + 21x = 30

Step 2 If the coefficient of x2 is not 1, divide both sides of the equation by the coefficient of x2.

Divide both sides by 3.

 x2 + 7x = 10
Step 3 Find the number that completes the square: Multiply the coefficient of x by . Square the result.

The coefficient of the x-term is 7.

 
Step 4 Add the result of Step 3 to both sides of the equation.

Add to both sides.

Simplify the right side.

The result is .

 

Step 5 Write the trinomial as the square of a binomial.
Step 6 Finish solving using the Square Root Property.

Use the Square Root Property.

For each equation, subtract from both sides and simplify the radical.
Step 7 Check each solution. We leave the check for you.  
The solutions of 3x2 - 30 = -21x are

Note:

To divide both sides of an equation by 3, we divide each term by 3, like this:

We can use the “plus or minus” symbol to write the solutions like this

 
All Right Reserved. Copyright 2005-2018