Solving the Equation: 3(x + 6)^2 = 75

The video tutorial guides viewers through solving the equation 3(x+6)^2=75. It begins by encouraging viewers to attempt solving it independently. The instructor then demonstrates the solution process: dividing both sides by 3, taking the square root of both sides, and subtracting 6 from both sides to isolate x. The tutorial concludes with verifying the solution by substituting the values back into the original equation.

What is the first step in solving the equation 3(x + 6)^2 = 75?

• Subtract 6 from both sides

• Add 6 to both sides

• Multiply both sides by 3

• Divide both sides by 3

After dividing both sides by 3, what is the resulting equation?

• (x + 6)^2 = 75

• (x + 6)^2 = 25

• 3(x + 6)^2 = 75

• 3(x + 6)^2 = 25

Why is it necessary to perform the same operation on both sides of an equation?

• To maintain the equality

• To change the equation

• To make the equation more complex

• To simplify the equation

What is the equation after dividing both sides by 3?

• (x + 6)^2 = 75

• (x + 6)^2 = 25

• 3(x + 6)^2 = 75

• 3(x + 6)^2 = 25

What operation is performed after isolating (x + 6)^2?

• Take the square root of both sides

• Subtract 6 from both sides

• Multiply both sides by 3

• Add 6 to both sides

What are the possible values of x after taking the square root?

• x = 11 or x = -11

• x = 1 or x = -1

• x = 5 or x = -5

• x = 6 or x = -6

What does taking the square root of both sides help achieve?

• It eliminates the square

• It isolates x

• It simplifies the equation

• It finds the possible values of x

What is the final step to solve for x?

• Add 6 to both sides

• Subtract 6 from both sides

• Multiply both sides by 3

• Divide both sides by 3

What are the final possible values of x?

• x = 5 or x = -5

• x = 6 or x = -6

• x = 1 or x = 11

• x = -1 or x = -11

What is the purpose of subtracting 6 from both sides?

• To isolate x

• To simplify the equation

• To eliminate the square

• To find the square root