Solving Quadratic Equations

The video tutorial guides viewers through solving an equation involving a square root. It begins by setting up the problem and isolating the radical expression. The instructor then demonstrates squaring both sides of the equation to eliminate the radical, leading to a quadratic equation. The tutorial continues with simplifying the equation and solving for x, followed by verifying the solution to ensure accuracy. The process is broken down into clear steps, making it easy to follow and understand.

What is the first step to solve the equation with a square root?

• Multiply both sides by 2

• Square both sides of the equation

• Add a constant to both sides

• Divide both sides by x

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

• Exponential equation

• Quadratic equation

• Cubic equation

• Linear equation

What operation is performed to simplify the quadratic equation?

• Subtract 5x squared from both sides

• Subtract 4x squared from both sides

• Multiply by 2 on both sides

• Add 5x squared to both sides

What is the result of taking the square root of both sides of the equation?

• x equals 2

• x equals the square root of 8

• x equals 8

• x equals 4

How can the square root of 8 be simplified?

• 2 times the square root of 4

• 8 times the square root of 2

• 4 times the square root of 2

• 2 times the square root of 2

What is the principal square root of 4?

• 2

• 1

• 4

• 3

What is the purpose of substituting the solution back into the original equation?

• To find a new solution

• To eliminate the square root

• To verify the solution is correct

• To simplify the equation further

What does the left-hand side simplify to when verifying the solution?

• 5 square roots of 2

• 2 square roots of 2

• 3 square roots of 2

• 4 square roots of 2

What is the value of 2x when x equals 2 square roots of 2?

• 5 square roots of 2

• 4 square roots of 2

• 3 square roots of 2

• 2 square roots of 2

What is the final conclusion after verifying the solution?

• The solution needs adjustment

• The solution is incorrect

• The solution is partially correct

• The solution is correct