Solving Quadratic Equations

The video tutorial explains how to solve a quadratic equation by first attempting to factor it and then using the method of completing the square. The instructor demonstrates the process of completing the square, isolating the variable, and solving for x, resulting in two possible solutions. The tutorial emphasizes understanding each step and encourages viewers to pause and reflect on the process.

What is the initial equation given in the problem?

• x^2 - 3x + 6 = 0

• x^2 + 3x + 6 = 0

• x^2 - 6x + 3 = 0

• x^2 + 6x + 3 = 0

Why does factoring not help in solving the equation?

• The equation is already factored.

• The sum and product of factors do not match the required values.

• Factoring is not applicable to quadratic equations.

• The equation has no real solutions.

What method is introduced after factoring fails?

• Substitution method

• Using the quadratic formula

• Completing the square

• Graphical method

What value is added and subtracted to complete the square?

• 12

• 9

• 3

• 6

What is the expression inside the parentheses after completing the square?

• (x + 3)^2

• (x - 6)^2

• (x - 3)^2

• (x + 6)^2

What operation is performed to isolate the squared term?

• Subtract 6 from both sides

• Add 6 to both sides

• Multiply both sides by 6

• Divide both sides by 6

What is the next step after isolating the squared term?

• Add 3 to both sides

• Multiply both sides by 3

• Subtract 3 from both sides

• Take the square root of both sides

What are the possible values for x after solving the equation?

• x = -3 ± √6

• x = 3 ± √3

• x = -3 ± √3

• x = 3 ± √6

What does the ± symbol indicate in the solution?

• The solution is exact.

• The solution is approximate.

• There are two possible solutions.

• There is only one solution.

How can the final solutions be expressed?

• x = 3 + √3 and x = 3 - √3

• x = 3 + √6 and x = 3 - √6

• x = -3 + √6 and x = -3 - √6

• x = -3 + √3 and x = -3 - √3