Solve. . √(w+25)-w=-5

Name: Problem 318, Chapter 8: Intermediate Algebra
Uploaded: 2022-09-25T14:02:28-08:00
Channel: Alison Rodriguez
Description: Solve. . √(w+25)-w=-5

Key Concepts

Extraneous Solutions

When eliminating radicals by raising both sides of an equation to a power, the process can introduce solutions that do not satisfy the original equation. Therefore, it is imperative to substitute any obtained solutions back into the original equation to verify their validity.

Domain Restrictions of Radical Functions

Radical functions, especially those involving even roots such as square roots, are defined only when their radicands are non-negative. This means that before solving the equation, one must consider the domain restrictions imposed by the radical to ensure that all potential solutions are within the acceptable range.

Radical Equations

Radical equations are equations in which the variable appears under a radical sign. The solution process typically involves isolating the radical expression and then raising both sides of the equation to a power to eliminate the radical, being cautious of the fact that this can introduce additional, spurious solutions.

Isolation and Elimination of the Radical

The common strategy to solve equations with radicals is to first isolate the radical on one side of the equation. Once isolated, both sides of the equation are raised to the power that corresponds to the radical (for example, squaring both sides for a square root) to remove the radical, simplifying the equation to a more standard algebraic form.

Transcript

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