Solve each equation. (2 x+6)^(1)/(2)=x

Name: Problem 84, Chapter 6: Intermediate Algebra
Uploaded: 2022-03-30T19:05:16-08:00
Duration: 1 min 20 s
Channel: Victor Salazar
Description: Solve each equation. (2 x+6)^(1)/(2)=x

Key Concepts

Radical Equations

Radical equations are equations that contain a variable within a radical, most commonly a square root. These equations require careful manipulation since the usual algebraic techniques may not directly apply to the radical portion of the equation, and special attention must be paid to any restrictions imposed by the presence of the radical.

Squaring Both Sides

Squaring both sides of an equation is a common strategy used to eliminate a square root or radical when solving radical equations. By applying this method, the equation is transformed into a polynomial equation, which may be easier to solve. However, this process can introduce extra solutions that weren't valid in the original radical equation.

Extraneous Solutions

Extraneous solutions are results that emerge from the process of solving an equation, particularly when both sides are squared, and do not satisfy the original equation. It is essential to substitute the obtained solutions back into the original equation to verify their validity.

Domain Restrictions

Domain restrictions refer to the limitations placed on the variable, especially in equations containing radicals. For a square root to be defined, the expression under the radical must be non-negative. Thus, these restrictions help determine the set of acceptable values and ensure that the operations performed during the solution process are valid.

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