Completing the Square

• 36

• -12

• -6

• 6

Answer explanation

To complete the square for x^2 - 12x, take half of -12 (which is -6) and square it, giving 36. Thus, the expression becomes (x - 6)^2 - 36 + 36, confirming the missing term is 36.

Answer explanation

To complete the square for the equation x^2 + 6x = 4, we add (6/2)^2 = 9 to both sides, resulting in (x + 3)^2 = 13. Thus, the correct equation is (x + 3)^2 = 13.

• 36

• 4

• 16

• -4

Answer explanation

To complete the square for the equation 3x^2 - 12x = 8, first factor out 3 from the left side: 3(x^2 - 4x). Then, take half of -4 (which is -2), square it to get 4, and add it to both sides. Thus, the number to add is 4.

Answer explanation

To complete the square for x^2 - 2x + 7 = 0, we rewrite it as (x - 1)^2 = -6. This shows the correct choice is (x - 1)^2 = -6, indicating complex solutions.

Solve by completing the square: k² − 16k + 21 = 0

Answer explanation

To complete the square for k^2 - 16k + 21 = 0, rewrite it as (k - 8)^2 = 43. Thus, k = 8 ± √43. The correct answer is k = 8 ± √43.

When do you use the plus or minus symbol?
±

• After taking the square root of both sides

• After adding the square to both sides

• After taking half of b

• After setting the equation equal to zero

Answer explanation

The plus or minus symbol (±) is used after taking the square root of both sides of an equation. This indicates that there are two possible solutions: one positive and one negative.

Write the following quadratic expression in completed square form...

x² + 4x + 10

• (x + 4)² + 6

• (x + 2)² + 6

• (x + 4)² - 6

• (x + 2)² - 6

Answer explanation

To complete the square for x² + 4x + 10, we take half of 4 (which is 2), square it (giving 4), and rewrite the expression as (x + 2)² + 6. Thus, the correct choice is (x + 2)² + 6.

Solve the following quadratics equation by completing the square...

x² - 10x - 5 = 0

• x = -5 ± √30

• x = 5 ± √30

• x = 30 ± √5

• x = -30 ± √5

Answer explanation

To solve x^2 - 10x - 5 = 0 by completing the square, rewrite it as (x - 5)^2 = 30. Thus, x = 5 ± √30, confirming the correct choice is x = 5 ± √30.

Solve the following quadratics equation by completing the square...

x² + 6x - 3 = 0

Answer explanation

To complete the square for x^2 + 6x - 3 = 0, rewrite it as (x + 3)^2 - 9 - 3 = 0. This simplifies to (x + 3)^2 = 12. Taking the square root gives x + 3 = ±2√3, leading to x = -3 ± 2√3, which matches the first choice.

Complete the Square and write in Vertex Form:

f(x) = x² + 6x + 5

• (x + 3)² - 4

• (x + 6)² - 4

• (x + 3x)² - 4

• (x + 3)² + 9

Answer explanation

To complete the square for f(x) = x^2 + 6x + 5, we rewrite it as f(x) = (x + 3)^2 - 4. This shows the vertex form, confirming the correct choice is (x + 3)^2 - 4.