Question

Solve the radical equation $\sqrt{3 x+10}=x+4$.

   Solve the radical equation $\sqrt{3 x+10}=x+4$.

Elementary Algebra

Elementary Algebra

Wade Ellis, Jr. 1st Edition

Chapter 10, Problem 67

Instant Answer

Solved by Expert Nidhi Garg

02/22/2021

Step 1

Step 1: Isolate the radical The radical is already isolated on the left side of the equation. Show more…

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Solve the radical equation $\sqrt{3 x+10}=x+4$.

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Key Concepts

Squaring Both Sides

Squaring both sides of an equation is a method used to eliminate a square root once it has been isolated. This step converts the radical equation into a polynomial equation. However, care must be taken as this process can introduce extraneous solutions that do not satisfy the original equation.

Extraneous Solutions

Extraneous solutions are potential answers that result from the process of eliminating radicals, typically through squaring both sides of the equation. These solutions may not satisfy the original equation. Therefore, it is necessary to check all derived solutions in the original equation to ensure they are valid.

Radical Equations

Radical equations are equations in which the variable is located inside a radical symbol, most commonly a square root. Solving these equations usually involves isolating the radical and then eliminating it by raising both sides of the equation to an appropriate power. This process requires careful handling to avoid mistakes and to account for possible extraneous solutions.

Isolating the Radical Expression

Isolating the radical expression is a critical step in solving radical equations. It involves rearranging the equation so that the radical is by itself on one side, which simplifies the process of eliminating the radical by subsequent algebraic operations.

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