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Scientific Notation
Notation and Symbols
Linear Equations and Inequalities in One Variable
Graphing Equations in Three Variables
What the Standard Form of a Quadratic can tell you about the graph
Simplifying Radical Expressions Containing One Term
Adding and Subtracting Fractions
Multiplying Radical Expressions
Adding and Subtracting Fractions
Multiplying and Dividing With Square Roots
Graphing Linear Inequalities
Absolute Value Function
Real Numbers and the Real Line
Monomial Factors
Raising an Exponential Expression to a Power
Rational Exponents
Multiplying Two Fractions Whose Numerators Are Both 1
Multiplying Rational Expressions
Building Up the Denominator
Adding and Subtracting Decimals
Solving Quadratic Equations
Scientific Notation
Like Radical Terms
Graphing Parabolas
Subtracting Reverses
Solving Linear Equations
Dividing Rational Expressions
Complex Numbers
Solving Linear Inequalities
Working with Fractions
Graphing Linear Equations
Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
Simplifying Rational Expressions
Linear Equations
Dividing Complex Numbers
Simplifying Square Roots That Contain Variables
Simplifying Radicals Involving Variables
Compound Inequalities
Factoring Special Quadratic Polynomials
Simplifying Complex Fractions
Rules for Exponents
Finding Logarithms
Multiplying Polynomials
Using Coordinates to Find Slope
Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
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Solving Equations with Radicals and Exponents

In the next example the even-root property is used to solve some equations that are a bit complicated.


Example 1

Using the even-root property

Solve each equation.

a) (x - 3)2 = 4

b) 2(x - 5)2 - 7 = 0

c) x4 - 1 = 80


a) (x - 3)2 = 4        
x - 3 = 4 or x - 3 = -2 Even-root property
x = 5 or x = 1 Add 3 to each side.

The solution set is {1, 5}.

b) 2(x - 5)2 - 7 = 0        
2(x - 5)2 = 7       Add 7 to each side.
(x - 5)2       Divide each side by 2.
x - 5 or x - 5 Even-root property
x or x
x or x  

The solution set is

c) x4 - 1 = 80
x4 = 81
x = ± = ± 3

The solution set is {-3, 3}.

You probably know hou to solve quadratic equations by factoring. The quadratic equations that we encounter in this chapter can be solved by using the even-root property as in parts (a) and (b) of Example 1. In the future you will learn general methods for solving any quadratic equation.

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