Question

Solve. Check for extraneous solutions. $\sqrt{-3 x-5}=x+3$

   Solve. Check for extraneous solutions.
$\sqrt{-3 x-5}=x+3$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 7, Problem 26

Instant Answer

Solved by Expert Amrita Bhasin

08/09/2019

Step 1

This gives us: \[(-3x - 5) = (x + 3)^2\] Show more…

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Solve. Check for extraneous solutions. $\sqrt{-3 x-5}=x+3$

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Key Concepts

Radical Equations

Radical equations are equations in which the variable is located under a radical sign. Solving these equations often involves isolating the radical and then eliminating it by raising both sides of the equation to an appropriate power, such as squaring when dealing with square roots. This process requires careful handling, as it can introduce additional solutions that may not be valid in the original equation.

Domain Restrictions

Domain restrictions refer to the limitations on the variable values that ensure expressions, especially those under radicals, remain valid. In the context of radical equations, the radicand (the expression under the radical) must be non-negative to yield real number results. Identifying and applying these restrictions is crucial to narrow down the possible solutions before proceeding with further algebraic manipulations.

Extraneous Solutions

Extraneous solutions are apparent answers that emerge during the process of solving an equation but do not satisfy the original equation. These often occur as a result of operations, such as squaring both sides of an equation, which can introduce non-valid solutions. It is essential to substitute back each potential solution into the original equation to verify its validity and discard any extraneous ones.

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