Solving Radical and Quadratic Equations

The video tutorial explains how to solve a radical equation involving square roots. It begins by squaring both sides of the equation to eliminate radicals, then combines like terms. Further squaring is used to remove remaining radicals, leading to a quadratic equation. The quadratic is solved by factoring, yielding two solutions. Finally, the solutions are verified by substituting them back into the original equation.

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

• Multiply both sides by a constant

• Square both sides of the equation

• Add a constant to both sides

• Take the cube root of both sides

After squaring both sides, what operation is performed on the left side?

• Simplifying the radicals

• Foiling the expression

• Combining constants

• Taking the derivative

What is the result of combining like terms on the left side after foiling?

• 5x + 2

• 6x + 3

• 7x + 4

• 8x + 4

What is the next step after isolating the radicals?

• Take the cube root of both sides

• Multiply both sides by a constant

• Square both sides again

• Add a constant to both sides

What type of equation is formed after removing the radicals?

• Cubic equation

• Quadratic equation

• Linear equation

• Exponential equation

What method is used to solve the quadratic equation?

• Graphing

• Using the quadratic formula

• Factoring by grouping

• Completing the square

What are the two numbers that multiply to 84 and add to -19?

• 6 and 13

• -6 and -13

• 7 and 12

• -7 and -12

What is the first solution obtained using the zero product property?

• x = 3

• x = 2

• x = 4

• x = 5

What is the second solution obtained using the zero product property?

• x = 7/4

• x = 6/4

• x = 5/4

• x = 8/4

How can you verify the solutions obtained?

• By substituting back into the original equation

• By graphing the equation

• By using a calculator

• By taking the derivative