step 1 We have problem number 51 in which we need to solve 2 minus x minus 4. 2 minus x under root unde

Solve. √(2-x)-4=6

Name: Problem 51, Chapter 14: Beginning and Intermediate Algebra
Uploaded: 2020-06-30T05:32:18-08:00
Duration: 1 min 10 s
Channel: Suman Saurav Thakur
Description: Solve. √(2-x)-4=6

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Key Concepts

Radical Equation

A radical equation is one in which the unknown variable appears inside a radical, most commonly a square root. To solve these equations, the radical is typically isolated first, which then allows for the elimination of the radical through raising both sides of the equation to a power that corresponds to the radical.

Domain Restrictions

When dealing with square roots, it is essential to consider domain restrictions. The expression under a square root must be non-negative in the context of real numbers, which limits the allowable values for the variable. This is a crucial step to ensure that all proposed solutions are valid.

Squaring Both Sides

Squaring both sides of an equation is a standard method for removing square roots in radical equations. However, caution must be exercised because squaring can potentially introduce solutions that do not satisfy the original equation. This step is instrumental in transitioning from a radical expression to a polynomial one.

Checking for Extraneous Solutions

After squaring an equation, extraneous solutions—solutions that arise from the process but do not satisfy the original equation—can appear. It is important to substitute any obtained solutions back into the original equation to verify that they are indeed valid within the initial constraints of the problem.

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