FreeAlgebra                             Tutorials! Home Polynomials Finding the Greatest Common Factor Factoring Trinomials Absolute Value Function A Summary of Factoring Polynomials Solving Equations with One Radical Term Adding Fractions Subtracting Fractions The FOIL Method Graphing Compound Inequalities Solving Absolute Value Inequalities Adding and Subtracting Polynomials Using Slope Solving Quadratic Equations Factoring Multiplication Properties of Exponents Completing the Square Solving Systems of Equations by using the Substitution Method Combining Like Radical Terms Elimination Using Multiplication Solving Equations Pythagoras' Theorem 1 Finding the Least Common Multiples Multiplying and Dividing in Scientific Notation Adding and Subtracting Fractions Solving Quadratic Equations Adding and Subtracting Fractions Multiplication by 111 Adding Fractions Multiplying and Dividing Rational Numbers Multiplication by 50 Solving Linear Inequalities in One Variable Simplifying Cube Roots That Contain Integers Graphing Compound Inequalities Simple Trinomials as Products of Binomials Writing Linear Equations in Slope-Intercept Form Solving Linear Equations Lines and Equations The Intercepts of a Parabola Absolute Value Function Solving Equations Solving Compound Linear Inequalities Complex Numbers Factoring the Difference of Two Squares Multiplying and Dividing Rational Expressions Adding and Subtracting Radicals Multiplying and Dividing Signed Numbers Solving Systems of Equations Factoring Out the Opposite of the GCF Multiplying Special Polynomials Properties of Exponents Scientific Notation Multiplying Rational Expressions Adding and Subtracting Rational Expressions With Unlike Denominators Multiplication by 25 Decimals to Fractions Solving Quadratic Equations by Completing the Square Quotient Rule for Exponents Simplifying Square Roots Multiplying and Dividing Rational Expressions Independent, Inconsistent, and Dependent Systems of Equations Slopes Graphing Lines in the Coordinate Plane Graphing Functions Powers of Ten Zero Power Property of Exponents The Vertex of a Parabola Rationalizing the Denominator Test for Factorability for Quadratic Trinomials Trinomial Squares Solving Two-Step Equations Solving Linear Equations Containing Fractions Multiplying by 125 Exponent Properties Multiplying Fractions Adding and Subtracting Rational Expressions With the Same Denominator Quadratic Expressions - Completing Squares Adding and Subtracting Mixed Numbers with Different Denominators Solving a Formula for a Given Variable Factoring Trinomials Multiplying and Dividing Fractions Multiplying and Dividing Complex Numbers in Polar Form Power Equations and their Graphs Solving Linear Systems of Equations by Substitution Solving Polynomial Equations by Factoring Laws of Exponents index casa mÃ­o Systems of Linear Equations Properties of Rational Exponents Power of a Product and Power of a Quotient Factoring Differences of Perfect Squares Dividing Fractions Factoring a Polynomial by Finding the GCF Graphing Linear Equations Steps in Factoring Multiplication Property of Exponents Solving Systems of Linear Equations in Three Variables Solving Exponential Equations Finding the GCF of a Set of Monomials

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:

# Completing the Square

The essential part of completing the square is to recognize a perfect square trinomial when given its first two terms. For example, if we are given x2 + 6x, how do we recognize that these are the first two terms of the perfect square trinomial x2 + 6x + 9? To answer this question, recall that x2 + 6x + 9 is a perfect square trinomial because it is the square of the binomial x + 3:

(x + 3)2 = x2 + 2 Â· 3x + 32 = x2 + 6x + 9

Notice that the 6 comes frommultiplying 3 by 2 and the 9 comes from squaring the 3. So to find the missing 9 in x2 + 6x, divide 6 by 2 to get 3, then square 3 to get 9. This procedure can be used to find the last term in any perfect square trinomial in which the coefficient of x2 is 1.

Rule for Finding the Last Term

The last term of a perfect square trinomial is the square of one-half of the coefficient of the middle term. In symbols, the perfect square trinomial whose first two terms are .

Review the rule for squaring a binomial: square the first term, find twice the product of the two terms, then square the last term. If you are still using FOIL to find the square of a binomial, it is time to learn the proper rule.

Example 1

Finding the last term

Find the perfect square trinomial whose first two terms are given. Solution

a) One-half of 8 is 4, and 4 squared is 16. So the perfect square trinomial is x2 + 8x + 16.

b) One-half of -5 is , and squared is . So the perfect square trinomial is .

c) One-half of is , and squared is . So the perfect square trinomial is d) One-half of is , and . So the perfect square trinomial is Another essential step in completing the square is to write the perfect square trinomial as the square of a binomial. Recall that

a2 + 2ab + b2 = (a + b)2 and a2 - 2ab + b2 = (a - b)2.

Example 2

Factoring perfect square trinomials

Factor each trinomial. Solution

a) The trinomial x2 + 12x + 36 is of the form a2 + 2ab + b2 with a = x and b = 6. So x2 + 12x + 36 = (x + 6)2. Check by squaring x + 6.

b) The trinomial is of the form a2 - 2ab + b2 with a = y and . So Check by squaring .

c) The trinomial is of the form a2 - 2ab + b2 with a = z and . So 