Solving Radical Equations and Quadratics

This video tutorial from YourTeacher.com demonstrates solving a math problem involving radicals. It begins by isolating the radical, then squaring both sides of the equation to eliminate it. The equation is set to zero and factored to find potential solutions. Finally, the solutions are checked against the original equation to verify their validity, concluding that only one solution is correct.

What is the first step in solving the given radical equation?

• Add 6 to both sides

• Multiply both sides by 2

• Isolate the radical on one side

• Divide both sides by 6

After isolating the radical, what operation is performed next?

• Taking the square root of both sides

• Squaring both sides of the equation

• Adding a constant to both sides

• Subtracting a constant from both sides

What is the result of expanding (x - 6) * (x - 6)?

• x^2 - 12x - 36

• x^2 - 6x + 36

• x^2 + 12x + 36

• x^2 - 12x + 36

What should be done after obtaining a quadratic equation?

• Solve for x directly

• Take the square root of both sides

• Set the equation equal to zero

• Multiply both sides by x

Which of the following is a factor of the equation x^2 - 3x + 36?

• x - 6

• x - 12

• x - 9

• x - 3

What are the potential solutions obtained after factoring?

• x = 9 or x = 6

• x = 12 or x = 6

• x = 9 or x = 4

• x = 6 or x = 3

Why is x = 4 not a valid solution when checked in the original equation?

• Because 4 is not in the domain of the function

• Because 2 + 6 does not equal 4

• Because 4 is not a real number

• Because 4 + 6 equals 10

Which value of x satisfies the original equation?

• x = 4

• x = 12

• x = 6

• x = 9