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
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:

# 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 â€” 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

Hereâ€™s how to use the Square Root Property to solve a quadratic equation.

Procedure â€” 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 - 72x2 = 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 © 2005-2018 Wednesday 21st of February