Solve. 6+√(c^2+3 c-9)=c

Name: Problem 37, Chapter 10: Beginning and Intermediate Algebra
Uploaded: 2020-06-27T18:32:57-08:00
Duration: 2 min 2 s
Channel: Amy Jiang
Description: Solve. 6+√(c^2+3 c-9)=c

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Key Concepts

Radical Equations

Radical equations are equations in which the variable appears under a root sign. Solving these equations typically involves isolating the radical term and then eliminating the radical by raising both sides of the equation to an appropriate power. This process must be handled carefully to ensure that all solutions obtained are valid.

Domain Considerations

When working with equations involving square roots, it is essential to consider the domain of the radical expression. This means ensuring that the expression under the square root is non-negative, as negative values would lead to non-real results in the context of real numbers.

Squaring Both Sides

Squaring both sides of an equation is a common method used to eliminate radicals from an equation. However, squaring can introduce extraneous solutions that do not satisfy the original equation, so it is necessary to verify each solution by substituting it back into the original equation.

Extraneous Solutions

Extraneous solutions are solutions that arise from the process of manipulating an equation, such as squaring both sides, but do not satisfy the original equation. To avoid incorrect answers, each candidate solution must be checked against the original equation to confirm its validity.

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