Solve quadratics by completing the square (exact answers)

Question 1

Solve x² + 12x + 7 = 0 by completing the square. Give exact answers.

• A. x = −6 ± √65
• B. x = −6 ± √29
• C. x = 6 ± √29
• D. x = −6 ± 29

Question 2

Rewrite x² − 6x − 9 = 0 as (x − 3)² = k. Find k.

Answer 

Question 3

Solve x² − 12x + 23 = 0 by completing the square. Give the smaller solution to 2 decimal places.

Answer 

Question 4

Solve x² + 6x − 4 = 0 by completing the square. Give exact answers.

• A. x = 3 ± √13
• B. x = −3 ± 13
• C. x = −6 ± √13
• D. x = −3 ± √13

Question 5

Rewrite x² + 12x + 5 = 0 as (x + 6)² = k. Find k.

Answer 

Question 6

Solve x² − 10x + 19 = 0 by completing the square. Give the larger solution to 2 decimal places.

Answer 

Question 7

Solve x² + 4x − 13 = 0 by completing the square. Give exact answers.

• A. x = −2 ± √21
• B. x = −4 ± √17
• C. x = −2 ± √17
• D. x = 2 ± √17

Question 8

Rewrite x² + 4x − 2 = 0 as (x + 2)² = k. Find k.

Answer 

Question 9

Solve x² + 8x + 1 = 0 by completing the square. Give the smaller solution to 2 decimal places.

Answer 

Question 10

Solve x² + 12x + 10 = 0 by completing the square. Give exact answers.

• A. x = −6 ± √26
• B. x = 6 ± √26
• C. x = −6 ± √62
• D. x = −6 ± 26

Question 11

Rewrite x² + 10x + 11 = 0 as (x + 5)² = k. Find k.

Answer 

Question 12

Solve x² − 2x − 21 = 0 by completing the square. Give the smaller solution to 2 decimal places.

Answer 

Question 13

Solve x² − 6x − 21 = 0 by completing the square. Give exact answers.

• A. x = −3 ± √30
• B. x = 3 ± 30
• C. x = 3 ± √39
• D. x = 3 ± √30

Question 14

Rewrite x² + 10x − 15 = 0 as (x + 5)² = k. Find k.

Answer 

Question 15

Solve x² − 2x − 21 = 0 by completing the square. Give the smaller solution to 2 decimal places.

Answer 

Question 16

Solve x² − 12x + 18 = 0 by completing the square. Give exact answers.

• A. x = 6 ± 3√2
• B. x = 6 ± 18
• C. x = 12 ± 3√2
• D. x = 6 ± √54