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 Using the Quadratic Formula

Example

Solve using the quadratic formula: 36x2 + 16 + 48x = 0

Solution

Step 1 Write the quadratic equation in standard form, ax2 + bx + c = 0. 36x2 + 16 + 48x = 0
On the left side, write the terms in decreasing powers of x.

Each term is divisible by 4. To simplify the calculations, divide both sides of the equation by 4.

Step 2 Identify the values of a, b, and c.

36x2 + 16 + 48x = 0

 

Step 3 Substitute the values of a, b, and c into the quadratic formula.
Step 4 Simplify.
Step 5 Check each solution.

We leave the check to you.

 

We say that is a solution of multiplicity two.

 

Example 2

Solve using the quadratic formula: x2 + 5 = 3x

Step 1 Write the quadratic equation in standard form, ax2 + bx + c = 0. x2 + 5 = 3x
Subtract 3x from both sides of the equation.

Step 2 Identify the values of a, b, and c.

Step 3 Substitute the values of a, b, and c into the quadratic formula.
Step 4 Simplify.
Notice the negative number under the square root symbol.

The radical does not represent a real number.

Therefore, the equation x2 + 5 = 3x has no real number solutions.

 
All Right Reserved. Copyright 2005-2018