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

Using the square root property it is possible to solve any quadratic equation written in the form
( x + b )2 = c . The key to setting these problems into the correct form is to recognize that
(x + b)2 is a perfect square trinomial. To turn the equation given into one that can be solved using the square root property, the following must be done:


Given : ax2 + bx + c = 0

1.) If a ≠ 1 divide both sides by a.
2.) Rewrite the equation so that both terms containing variables are on one side of the equation and the constant is on the other.
3.) Take half of the coefficient of x and square it.
4.) Add the square to both sides.
5.) One side should now be a perfect square trinomial.
Write it as the square of a binomial.
6.) Use the square root property to complete the solution.
 

Example 1. Solve 2a2 – 4a – 5 = 0 by completing the square.

Solution
Step 1: Divide the equation by a

Step 2: Move the constant term to the right side of the equation

Step 3: Take half of the coefficient for x and square it

Step 4: Add the square to both sides of the equation

 

Example 1 (Continued):
Step 5: Factor the perfect square trinomial

Step 6: Take the square root of both sides

 

Example 2. Solve 9a2– 24a = -13 by completing the square.

Solution
Step 1: Divide the equation by a

Step 2: Move the constant term to the right side of the equation

Example 2 (Continued):

Step 3: Take half of the coefficient for x and square it

Step 4: Add the square to both sides of the equation

Step 5: Factor the perfect square trinomial

Step 6: Take the square root of both sides

Example 3. Solve 9x2 – 30x + 29 by completing the square.

Solution
Step 1: Divide the equation by a

Step 2: Move the constant term to the right side of the equation

Step 3: Take half of the coefficient for x and square it

Step 4: Add the square to both sides of the equation

Step 5: Factor the perfect square trinomial

Example 3 (Continued):
Step 6: Take the square root of both sides

All Right Reserved. Copyright 2005-2024