Algebra Tutorials!
   
Home
About Us




TUTORIALS:

Absolute Values
Solving Two-Step Equations Algebraically
Multiplying Monomials
Factoring Trinomials
Solving Quadratic Equations
Power Functions and Transformations
Composition of Functions
Rational Inequalities
Equations of Lines
Graphing Logarithmic Functions
Elimination Using Multiplication
Multiplying Large Numbers
Multiplying by 11
Graphing Absolute Value Inequalities
Polynomials
The Discriminant
Reducing Numerical Fractions to Simplest Form
Addition of Algebraic Fractions
Graphing Inequalities in Two Variables
Adding and Subtracting Rational Expressions with Unlike Denominators
Multiplying Binomials
Graphing Linear Inequalities
Properties of Numbers and Definitions
Factoring Trinomials
Relatively Prime Numbers
Point
Inequalities
Rotating a Hyperbola
Writing Algebraic Expressions
Quadratic and Power Inequalities
Solving Quadratic Equations by Completing the Square
BEDMAS & Fractions
Solving Absolute Value Equations
Writing Linear Equations in Slope-Intercept Form
Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
Solving Absolute Value Equations
Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
Solving Equations with a Fractional Exponent
Simple Trinomials as Products of Binomials
Equivalent Fractions
Multiplying Polynomials
Slope
Graphing Equations in Three Variables
Properties of Exponents
Graphing Linear Inequalities
Solving Cubic Equations by Factoring
Adding and Subtracting Fractions
Multiplying Whole Numbers
Straight Lines
Solving Absolute Value Equations
Solving Nonlinear Equations
Factoring Polynomials by Finding the Greatest Common Factor
Logarithms
Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
Solving Equations
Factoring Polynomials
Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
Square Roots
Adding Polynomials
Arithmetic with Positive and Negative Numbers
Solving Equations
Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
Plotting a Point
Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Percents
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Radicals
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
Dividing Polynomials by Monomials
Factoring Trinomials
Introduction to Fractions
Square Roots
   

Solving Quadratic Equations Using the Square Root Property

The Square Root Property can be used to solve a quadratic equation written in the form x2 = a.

 

Property — Square Root Property

If x2 = a, then

Here, a is a nonnegative real number.

Examples

If x2 = 7, then

If (w + 6)2 = 3, then

Here’s how to use the Square Root Property to solve a quadratic equation.

 

Procedure — To Solve a Quadratic Equation Using the Square Root Property

Step 1 Write the equation in the form x2 = a.

Step 2 Use the Square Root Property.

Step 3 Write each answer in simplified form.

Step 4 Check each answer.

 

Example 1

Solve using the Square Root Property: x2 - 72 = 0

Solution

Step 1 Write the equation in the form x2 = a.

Add 72 to both sides.

x2 - 72

x2

= 0

= 0

Step 2 Use the Square Root Property.
Step 3 Write each answer in simplified form.

Simplify each square root.

Step 4 Check each answer.    

So, the equation x2 - 72 = 0 has two solutions, and -.

 

Example 2

Solve using the Square Root Property: -4x2 + 64 = 0

Solution

Step 1 Write the equation in the form x2 = a.

Subtract 64 from both sides.

Divide both sides by -4.

 -4x2 + 64

-4x2

x2

= 0

= -64

= 16

Step 2 Use the Square Root Property.
Step 3 Write each answer in simplified form.

Step 4 Check each answer.

We leave the check to you.

x = 4 or x = -4

So, the two solutions of -4x2 + 64 = 0 are 4 and -4.

Note:

Another way to write the solution is:

Copyrights © 2005-2014
Wednesday 30th of July