Free Algebra
Tutorials!
 
Home
Systems of Linear Equations and Problem Solving
Solving Quadratic Equations
Solve Absolute Value Inequalities
Solving Quadratic Equations
Solving Quadratic Inequalities
Solving Systems of Equations Row Reduction
Solving Systems of Linear Equations by Graphing
Solving Quadratic Equations
Solving Systems of Linear Equations
Solving Linear Equations - Part II
Solving Equations I
Summative Assessment of Problem-solving and Skills Outcomes
Math-Problem Solving:Long Division Face
Solving Linear Equations
Systems of Linear Equations in Two Variables
Solving a System of Linear Equations by Graphing
Ti-89 Solving Simultaneous Equations
Systems of Linear Equations in Three Variables and Matrix Operations
Solving Rational Equations
Solving Quadratic Equations by Factoring
Solving Quadratic Equations
Solving Systems of Linear Equations
Systems of Equations in Two Variables
Solving Quadratic Equations
Solving Exponential and Logarithmic Equations
Solving Systems of Linear Equations
Solving Quadratic Equations
Math Logic & Problem Solving Honors
Solving Quadratic Equations by Factoring
Solving Literal Equations and Formulas
Solving Quadratic Equations by Completing the Square
Solving Exponential and Logarithmic Equations
Solving Equations with Fractions
Solving Equations
Solving Linear Equations
Solving Linear Equations in One Variable
Solving Linear Equations
SOLVING QUADRATIC EQUATIONS USING THE QUADRATIC FORMULA
SOLVING LINEAR EQUATIONS
 
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

An equation that can be simplified to the form is called a quadratic equation. If the equation is already simplified to this form we say it is in standard form. We have already investigated two techniques for solving quadratic equations: extraction of roots (which works if there is no linear term) and factoring. Neither technique is practical in all cases. We will now investigate a technique that is practical more generally.

Using the Quadratic Formula
The quadratic formula lets us find the solutions of a quadratic equation when it is written in standard
form. The plus or minus symbol (±) allows us to represent both solutions in a single expression. Lets take a look at an example to see how it works.

Example: Use the quadratic formula to find the solutions to the equation

Solution: First we identify the coefficients a, b and c for this equation: a = 3, b = 4 and c = −5. Then we substitute these values for a, b and c in the formula:

Let’s represent each solution separately and use our calculators to approximate the solutions.

We can enter each of these solutions into our graphing calculators with a single entry but we must pay careful attention to the order of operations. Let’s start with the first solution. Enter it into your calculator as follows:

When you push enter the calculator should return the value
.7862996478

This is an approximation of the first solution. Now we turn our attention to the second solution. Press 2nd Enter to bring up the previous entry:

The entry for the second solution is identical except that the addition that I’ve highlighted above should be changed to a subtraction:

When you push enter the calculator should return the value

−2.119632981

So the solutions to the equation are approximately x = .7862996478 and x = −2.119632981

All Right Reserved. Copyright 2005-2017