Solve. 18 x 2-6 x+1-√(=) 3 x

Name: Problem 52, Chapter 8: Elementary Algebra
Uploaded: 2022-02-03T19:14:31-08:00
Duration: 43 s
Channel: James Kiss
Description: Solve. 18 x 2-6 x+1-√(=) 3 x

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Key Concepts

Radical Equations

Radical equations involve an expression with a variable under a root. A common approach is to isolate the radical on one side and then raise both sides of the equation to a power that eliminates the radical. This method transforms the equation into one that is often easier to solve, but it requires caution because raising both sides to a power may introduce solutions that do not satisfy the original equation.

Extraneous Solutions

Extraneous solutions are potential answers that result from algebraic manipulations, such as squaring both sides of an equation, which do not actually satisfy the original equation. In the context of radical equations, it is important to substitute any found solutions back into the original equation to verify their validity.

Quadratic Equations

Quadratic equations are polynomial equations of degree two that may naturally appear after eliminating radicals from an equation. These equations can often be solved using factoring approaches, the quadratic formula, or completing the square. Recognizing and solving the resulting quadratic form is a key part of solving more complex equations that include radicals.

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