Solving Radical Equations with Factoring Techniques

What is the first step in solving equations involving square roots?

• Isolate the square root

• Square both sides immediately

• Set the equation to zero

• Factor the equation

What does squaring the expression (x + 5) result in?

• 5x + 25

• x^2 + 10x + 25

• x^2 + 5x

• x^2 + 25

What method is used to simplify (x + 5)^2?

• Distributive

• FOIL

• Factoring

• Division

After squaring both sides and simplifying, what type of equation do we obtain?

• Linear

• Exponential

• Quadratic

• Cubic

How do you prepare a quadratic equation for factoring?

• Set the equation equal to zero

• Divide each term by x

• Add a constant to both sides

• Multiply through by the leading coefficient

Which pair of numbers multiplies to 18 and adds up to 9?

• 2 and 9

• 3 and 6

• 1 and 18

• 4 and 5

What are the solutions to the equation x^2 + 9x + 18 = 0 after factoring?

• x = -6, x = -3

• x = 6, x = 3

• x = -9, x = -2

• x = 9, x = 2

Why is it important to check the solutions of a quadratic equation?

• To ensure the solutions satisfy the original equation

• To convert the solutions to higher degrees

• To practice more algebra

• To make the solutions complex

What is an extraneous solution in the context of solving equations?

• A solution that simplifies the equation

• A solution that does not satisfy the original equation

• The only solution to the equation

• A solution that makes the equation undefined

Which solution was identified as extraneous in the problem discussed?

• x = 6

• x = 3

• x = -3

• x = -6