Completing the Square Quiz

What is the first step in completing the square for a quadratic equation?

• Isolate the x terms on one side

• Multiply both sides by a constant

• Add a constant to both sides

• Take the square root of both sides

How do you determine the number to add to both sides when completing the square?

• Square the a value

• Take half of the b value and square it

• Double the b value

• Add the a and c values

What is the result of simplifying the square root of 32?

• 4√2

• 5√2

• 3√2

• 6√2

When completing the square, why might you divide the entire equation by a common factor?

• To eliminate the constant term

• To change the sign of the equation

• To simplify the coefficients

• To make the equation easier to factor

What is the solution to x^2 + 6x + 6 = 0 after completing the square?

• x = -3 ± √6

• x = 3 ± √3

• x = -3 ± √3

• x = 3 ± √6

How do you handle a negative number under the square root when solving a quadratic equation?

• Add a constant to make it positive

• Use the imaginary unit i

• Ignore the negative sign

• Multiply by -1

What is the imaginary unit 'i' equivalent to?

• √1

• √-1

• √2

• √0

In the equation x^2 + 4x + 28 = 0, what is the first step to solve it by completing the square?

• Multiply by 2

• Add 28 to both sides

• Subtract 28 from both sides

• Divide by 4

What is the final solution for x^2 + 4x + 28 = 0 after completing the square?

• x = -2 ± 2i√6

• x = -2 ± i√6

• x = 2 ± 2i√6

• x = 2 ± i√6

What is the purpose of completing the square in solving quadratic equations?

• To find the vertex of the parabola

• To solve for x by making a perfect square trinomial

• To eliminate the x term

• To convert the equation to vertex form