Solving Radical and Quadratic Equations

This video tutorial covers solving radical equations, including those that lead to quadratic equations. It begins with a review of solving quadratic equations by factoring, ensuring equations are set to zero, and finding solutions. The tutorial then progresses to solving radical equations by isolating the radical, squaring both sides, and checking solutions in the original equation. It also addresses complex cases involving binomials and unique scenarios where solutions may be extraneous.

What is the first step in solving a quadratic equation by factoring?

• Set the equation equal to zero

• Add all terms to one side

• Divide all terms by the smallest coefficient

• Multiply all terms by the greatest common factor

When solving a radical equation that results in a quadratic, what should you do after isolating the radical?

• Subtract the radical from both sides

• Add a constant to both sides

• Square both sides of the equation

• Multiply both sides by the radical

In the equation \( \sqrt{42 - x} = x \), what is the correct solution?

• x = 7

• x = 0

• x = 6

• x = -7

What is the solution to the equation \( y^2 = 18y - 81 \)?

• y = 9

• y = -9

• y = 0

• y = 18

How do you handle a radical equation where the radical is not isolated?

• Add or subtract terms to isolate the radical

• Divide both sides by the radical

• Multiply both sides by the radical

• Square both sides immediately

What is the solution to the equation \( v + 6 = \sqrt{3v + 58} \)?

• v = 2

• v = -11

• v = -2

• v = 6

In the equation \( n + 5 = \sqrt{8n + 24} \), what is the correct solution?

• n = 0

• n = 1

• n = -1

• n = 5

What should you do if you find an extraneous solution when solving a radical equation?

• Ignore it and use the other solutions

• Recalculate the entire equation

• Verify it against the original equation

• Use it as the final answer

What is the result of squaring a binomial \((x - 3)^2\)?

• x^2 - 3x + 9

• x^2 - 9

• x^2 + 6x + 9

• x^2 - 6x + 9

What is the correct approach to solve \( \sqrt{8 - 2b} = b - 4 \)?

• Multiply both sides by 2

• Add 4 to both sides and solve

• Subtract 8 from both sides

• Isolate the radical and then square both sides