Extraneous Solutions - Solving Equations - Farwell

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Solving Equations

Extraneous Solutions

Sometimes when solving math problems the process of simplifying creates a different domain than the original equation. This creates an invalid solution known as extraneous. An extraneous solution is the solution of the simplified form of an equation that does not satisfy the original equation and needs to be eliminated.

It is necessary to check for extraneous solutions when the original equation has a restricted domain. The equation in the next example contains a square root. Since even root functions are restricted to values greater than or equal to zero, any equation involving even roots or their corresponding fractional exponent should be checked for extraneous solutions.

There are other functions that require checks of extraneous solutions, but those will be discussed in other courses.

◀︎ Adding & Subtracting Jump to... Jump to... Creation of Michigan Algebra I Pre-Assessment: Linear Multiple Choice Paper Pre-Assessment: Linear Unit Multiple Choice Paper Pre-Assessment: Linear Unit Multiple Choice Key Overview Independent & Dependent Variables Function Notation Solving for a Variable Finding Zeros Slope-Intercept Form Standard Form Point-Slope Form Domain & Range Inverses Parallel & Perpendicular Lines Tables Graphs Applications Solving Graphing Modeling Graphing Solving Using Substitution Solving Using Elimination Modeling Post-Assessment: Linear Multiple Choice Paper Post-Assessment: Linear Unit Multiple Choice Paper Post-Assessment: Linear Unit Multiple Choice Key Paper Post-Assessment: Linear Unit Short Answer Paper Post-Assessment: Linear Unit Short Answer Key Pre-Assessment: Quadratic Multiple Choice Paper Pre-Assessment: Quadratic Unit Multiple Choice Paper Pre-Assessment: Quadratic Unit Multiple Choice Key Overview Characteristics Function Notation Adding & Subtracting Multiplying & Dividing Graphing Using Square Roots Factoring Completing the Square Quadratic Formula Foundations Vertex Form Transformations Factored Form Standard Form Domain & Range Inverses Tables Graphs Applications Which Function Is It? Post-Assessment: Quadratic Multiple Choice Paper Post-Assessment: Quadratic Unit Multiple Choice Paper Post-Assessment: Quadratic Unit Multiple Choice Key Paper Post-Assessment: Quadratic Unit Short Answer Paper Post-Assessment: Quadratic Unit Short Answer Key Pre-Assessment: Polynomial Multiple Choice Paper Pre-Assessment: Polynomial Unit Multiple Choice Paper Pre-Assessment: Polynomial Unit Multiple Choice Key Overview Characteristics Foundations Graphical Behavior Domain & Range Transformations Inverses Graphically Factor by Grouping Factoring Special Patterns Tables Graphs Applications Which Function Is It? Post-Assessment: Polynomial Multiple Choice Paper Post-Assessment: Polynomial Unit Multiple Choice Paper Post-Assessment: Polynomial Unit Multiple Choice Key Paper Post-Assessment: Polynomial Unit Short Answer Paper Post-Assessment: Polynomial Unit Short Answer Key Pre-Assessment: Power & Exponential Multiple Choice Paper Pre-Assessment: Power & Exponential Unit Multiple Choice Paper Pre-Assessment: Power & Exponential Unit Multiple Choice Key Overview Power & Exponential Functions Graphing Inverses Multipying & Dividing Rules Remaining Power Rules Zero & Negative Exponents Fractional Exponents Overview Multiplying & Dividing Adding & Subtracting Graphing Graphical Behavior Transformations Domain & Range Inverses Tables Graphs Exponential Growth Exponential Decay Compound Interest Which Function Is It? Post-Assessment: Power & Exponential Multiple Choice Paper Post-Assessment: Power & Exponential Unit Multiple Choice Paper Post-Assessment: Power & Exponential Unit Multiple Choice Key Paper Post-Assessment: Power & Exponential Unit Short Answer Paper Post-Assessment: Power & Exponential Unit Short Answer Key Pre-Assessment: Bivariate Multiple Choice Paper Pre-Assessment: Bivariate Unit Multiple Choice Paper Pre-Assessment: Bivariate Unit Multiple Choice Key Overview Displaying Data Plotting Data Pearson's Correlation Coefficient Linear Regression Piecewise Absolute Value Recursive Applications Which Function Is It? Post-Assessment: Bivariate Multiple Choice Paper Post-Assessment: Bivariate Unit Multiple Choice Paper Post-Assessment: Bivariate Unit Multiple Choice Key Paper Post-Assessment: Bivariate Unit Short Answer Paper Post-Assessment: Bivariate Unit Short Answer Key Algebra I Final Exam Algebra I Final Exam Key Graphing ▶︎ Skip Table of contents

Table of contents

• Introduction
• Basic Equations
  • Video Lesson
• Radicals on Both Sides
  • Video Lesson
• Extraneous Solutions
  • Example
  • Video Lesson
• Rational Exponents
  • Video Lesson
• Guided Practice
• Practice
  • Answer Key
• Sources