Solving Quadratic Equations

The video tutorial guides viewers through solving a quadratic equation by first transforming it to equal zero. It explains why factoring is initially not useful and highlights the importance of recognizing perfect squares. The tutorial then demonstrates how to factor the equation and solve for x, resulting in x equaling 7/3.

What is the initial equation given in the problem?

• 9x^2 - 42x + 29 = -20

• 9x^2 - 42x + 49 = -20

• 9x^2 - 42x + 49 = 0

• 9x^2 - 42x + 29 = 0

Why is factoring the left-hand side directly not helpful?

• Because it leads to an incorrect solution

• Because the product of binomials is not equal to zero

• Because it results in a complex number

• Because it simplifies the equation too much

What is the first step to transform the equation?

• Divide both sides by 9

• Multiply both sides by 2

• Add 20 to both sides

• Subtract 20 from both sides

What is the resulting equation after adding 20 to both sides?

• 9x^2 - 42x + 29 = 20

• 9x^2 - 42x + 49 = 0

• 9x^2 - 42x + 29 = 0

• 9x^2 - 42x + 49 = 20

What indicates that the quadratic expression might be a perfect square?

• The expression is already factored

• The numbers 9 and 49 are perfect squares

• The equation is linear

• The coefficients are prime numbers

How can the expression 9x^2 - 42x + 49 be factored?

• (3x + 7)^2

• (3x + 7)(3x - 7)

• (3x - 7)(3x + 7)

• (3x - 7)^2

What is the next step after factoring the expression as a perfect square?

• Set each factor equal to 20

• Set the expression equal to zero

• Add 7 to both sides

• Multiply the factors

What equation do we solve to find the value of x?

• 3x - 7 = 0

• 3x - 7 = 7

• 3x + 7 = 7

• 3x + 7 = 0

What is the value of x after solving the equation?

• x = 3/7

• x = -3/7

• x = -7/3

• x = 7/3

What operation is performed to isolate x in the equation 3x = 7?

• Multiply both sides by 3

• Divide both sides by 3

• Subtract 3 from both sides

• Add 3 to both sides