Solve. √(7 x+4)=x+2

Name: Problem 64, Chapter 14: Beginning and Intermediate Algebra
Uploaded: 2020-06-30T03:35:04-08:00
Duration: 3 min 23 s
Channel: Suman Saurav Thakur
Description: Solve. √(7 x+4)=x+2

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Key Concepts

Extraneous Solutions

Extraneous solutions are results that arise during the process of solving an equation, particularly when both sides are squared, and they do not satisfy the original equation. Verifying each potential solution in the original equation is crucial to discard these invalid responses.

Radical Equations

Radical equations are equations in which the variable is contained inside a radical, most commonly a square root. These equations must be handled with extra care, as operations like raising both sides of an equation to a power may introduce additional, invalid solutions.

Domain Restrictions

When solving equations involving radicals, particularly square roots, it is necessary to consider the domain restrictions. For square roots, the expression inside (the radicand) must be nonnegative, ensuring that all potential solutions fall within the set of real numbers.

Squaring Both Sides

Squaring both sides of an equation is a typical method used to eliminate radicals, thus simplifying the equation into a more standard algebraic form. This technique can make the equation easier to solve, but it requires subsequent verification of solutions due to potential introduction of extraneous answers.

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