Solving Quadratic Equations Using Substitution

The video tutorial explains how to solve a quadratic equation using substitution. It begins by identifying the equation's quadratic form and introduces substitution to simplify it. The tutorial then demonstrates factoring the equation and solving for the variable r. Finally, it verifies the solutions by substituting them back into the original equation, ensuring they satisfy the equation.

What is the initial form of the equation given in the problem?

• r^2 + 2r - 3 = 0

• (r + 4)^2 + 2(r + 4) - 3 = 0

• r^2 + 4r + 2 = 0

• (r + 4)^2 - 3 = 0

What substitution is made to simplify the equation?

• u = r - 4

• u = r^2 + 4

• u = r + 4

• u = 2r + 4

After substitution, what is the form of the quadratic equation?

• u^2 + 2u - 3 = 0

• u^2 - 2u + 3 = 0

• u^2 + 3u - 2 = 0

• u^2 - 3u + 2 = 0

What are the factors of the quadratic equation in terms of u?

• (u + 4)(u - 1)

• (u + 2)(u - 2)

• (u + 3)(u - 1)

• (u + 1)(u - 3)

What is the next step after factoring the equation in terms of u?

• Solve for u

• Substitute back to solve for r

• Verify the solution

• Graph the equation

What are the simplified factors in terms of r?

• (r + 5)(r + 2)

• (r + 7)(r + 3)

• (r + 6)(r + 4)

• (r + 8)(r + 2)

What are the solutions for r after solving the linear equations?

• r = -5 and r = -2

• r = -6 and r = -4

• r = -7 and r = -3

• r = -8 and r = -2

How do you verify the solutions obtained for r?

• By solving another equation

• By substituting them into the factored form

• By checking if they satisfy the original equation

• By graphing the solutions

What should the left side of the equation equal when the correct solutions are substituted back?

• 1

• -1

• 2

• 0

What is the purpose of verifying the solutions?

• To factor the equation again

• To simplify the equation further

• To find new solutions

• To ensure the solutions are correct