Solving Quadratic Equations by Substitution

The video tutorial explains how to solve a quadratic equation using substitution. It begins by introducing the concept of substitution to simplify the equation, followed by factoring the simplified equation. The tutorial then demonstrates solving for the variable p and finding the solutions. Finally, it verifies that the solutions satisfy the original equation, ensuring the correctness of the method used.

What is the first step in solving a quadratic equation using substitution?

• Set the equation to zero

• Introduce a new variable

• Combine like terms

• Clear the parentheses

In the substitution method, what does 'u' represent?

• The factors of the equation

• The solution to the equation

• The variable 'p' plus two

• The original equation

What is the purpose of setting the equation to zero?

• To simplify the equation

• To find the factors

• To solve for 'u'

• To eliminate variables

Which of the following is a factor of the equation in terms of 'u'?

• u - 5

• u - 1

• u + 3

• u + 5

After factoring, what is the next step in solving for 'p'?

• Perform another substitution

• Clear the parentheses

• Combine like terms

• Set each factor to zero

What are the solutions for 'p' after substitution?

• p = 0 and p = 5

• p = 3 and p = -3

• p = 2 and p = -2

• p = 1 and p = -1

Why is it important to verify the solutions?

• To ensure the equation is simplified

• To confirm the solutions satisfy the original equation

• To check if the factors are correct

• To find additional solutions

What is the result when substituting p = -3 into the original equation?

• 1 = 1

• 0 = 0

• 5 = 5

• 3 = 3

What is the result when substituting p = 3 into the original equation?

• 30 = 30

• 25 = 25

• 15 = 15

• 10 = 10

What is the final step in solving a quadratic equation using substitution?

• Set the equation to zero

• Factor the equation

• Introduce a new variable

• Verify the solutions