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!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

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