Solve. -√(2 x)+4=-6

Name: Problem 25, Chapter 7: Intermediate Algebra
Uploaded: 2020-07-19T00:36:21-08:00
Duration: 52 s
Channel: Vishal Parmar
Description: Solve. -√(2 x)+4=-6

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Key Concepts

Isolating the Radical Term

This concept involves rearranging the equation to have the radical by itself on one side. In equations that include square roots or other radical expressions, isolating the radical helps set up the next steps in eliminating the radical by applying an inverse operation, such as raising both sides of the equation to an appropriate power.

Squaring Both Sides of an Equation

Once the radical term is isolated, squaring both sides is a common method to remove the square root, converting the equation into a polynomial form. This process simplifies the equation and allows for standard algebraic techniques to be used in solving for the unknown variable.

Extraneous Solutions

Squaring both sides can introduce solutions that satisfy the squared equation but not the original equation. It is important to verify each solution in the original equation to ensure they are valid and not just artifacts of the squaring process.

Domain Restrictions for Radical Expressions

When working with square roots or other radicals in equations, the domain of the variable is restricted by the requirement that the expression inside the radical must be non-negative. This consideration ensures that the equation remains within the realm of real numbers and that any proposed solutions are valid within the context of the problem.

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