Solving a Radical Equation When You Have One Extraneous Solution

The video tutorial guides students through solving a radical equation. It begins with isolating the radical expression and proceeds to square both sides to eliminate the square root. The instructor explains how to expand the binomial and form a perfect square trinomial. The equation is then set to zero, and solutions are found using factoring. The importance of checking solutions for extraneous results is emphasized, with examples provided to illustrate the process.

What is the first step in solving an equation with a radical expression?

• Add a constant to both sides

• Divide both sides by a variable

• Isolate the radical expression

• Multiply both sides by a constant

When you have both linear and quadratic terms in an equation, what should you do first?

• Combine all terms on one side

• Set the equation equal to zero

• Multiply all terms by a constant

• Divide all terms by the highest degree term

Which method is NOT typically used to solve a quadratic equation?

• Quadratic formula

• Graphing

• Completing the square

• Factoring

Why is it important to check your solutions in the context of radical equations?

• To ensure the solution is not extraneous

• To find additional solutions

• To simplify the equation further

• To verify the equation is linear

What happens if a solution is extraneous?

• It must be discarded

• It is still a valid solution

• It needs to be simplified further

• It becomes the only solution