Solve. x^2+6 x=4 √(x^2+6 x)

Name: Problem 100, Chapter 7: Intermediate Algebra
Uploaded: 2020-07-17T18:34:20-08:00
Duration: 5 min 26 s
Channel: Vishal Parmar
Description: Solve. x^2+6 x=4 √(x^2+6 x)

Key Concepts

Extraneous Solutions

Extraneous solutions are solutions that emerge from the process of algebraically manipulating an equation, particularly when both sides of an equation are squared. It is necessary to substitute back potential solutions into the original equation to verify their validity.

Domain Restrictions

When dealing with square roots, it is essential to consider domain restrictions. The expression inside the square root must be non-negative, as square roots of negative numbers are not defined in the set of real numbers.

Quadratic Equations

Quadratic equations are polynomials of degree two and typically have two solutions, which can be found using factoring, completing the square, or the quadratic formula. In the context of a substitution, solving the resulting quadratic equation is a key step in finding the original variable's values.

Substitution

Substitution is used to simplify an equation by replacing a more complicated expression with a single variable. In this problem, the expression under the square root and its square, x² + 6x, is replaced by a new variable, allowing the equation to be expressed in a simpler form.

Radical Equations

Radical equations involve the unknown variable within a radical sign. Special care must be taken when solving them because operations like squaring both sides can introduce additional, extraneous solutions that do not satisfy the original equation.

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