Exploring Adding and Subtracting Rational Expressions

What is the 'Magic Square Number' in the context of completing the square?

• The coefficient of x after dividing the equation by a.

• The number obtained by squaring half of the coefficient of x.

• The constant term added to both sides of the equation.

• The result of squaring the leading coefficient.

What is the first step in solving a quadratic equation by completing the square when the leading coefficient is greater than one?

• Take half of the coefficient of x and square it.

• Rewrite the equation in the form ax^2 + bx = c.

• Factor the perfect square trinomial.

• Divide the equation by the leading coefficient.

How do you find the solutions after factoring the perfect square trinomial?

• By dividing both sides by the leading coefficient.

• By taking the square root of both sides.

• By adding the constant term to both sides.

• By subtracting the constant term from both sides.

What is the solution for x when the equation is x^2 + 2x + 1 = 9/4?

• x = -1/2 and x = -3/2

• x = 2 and x = -4

• x = 3/2 and x = -3/2

• x = 1/2 and x = -5/2

After dividing the equation by the leading coefficient, what form does the equation take?

• ax^2 + bx + c = 0

• x^2 + bx = c

• ax^2 = bx + c

• x^2 + c = bx

How do you handle the square root of a negative number in the context of completing the square?

• It indicates the equation has no real solutions.

• By treating it as an imaginary number.

• By using the absolute value.

• By converting it to an irrational number.

What does it mean when a quadratic equation has irrational solutions?

• The solutions cannot be expressed as fractions.

• The solutions are complex numbers.

• The solutions are perfect squares.

• The solutions can be expressed as simple fractions.

What is the result of adding the 'Magic Square Number' to both sides of the equation x^2 - 2x = 31?

• x^2 - 2x + 1 = 32

• x^2 - 2x + 2 = 33

• x^2 - 2x - 1 = 30

• x^2 - 2x + 4 = 35

What is the simplified form of the square root of 32?

• 4√3

• 4√2

• 6√2

• 5√2

What is the final form of the solution for the equation x^2 - 2x + 1 = 32?

• x = 1 ± 4√2

• x = 4 ± 4√2

• x = 2 ± 4√2

• x = 3 ± 4√2