Solve quadratics by completing the square (exact answers)

Question 1

Solve x² + 10x + 4 = 0 by completing the square. Give the smaller solution to 2 decimal places.

Answer 

Question 2

Solve x² − 2x − 12 = 0 by completing the square. Give exact answers.

• A. x = −1 ± √13
• B. x = 1 ± √14
• C. x = 2 ± √13
• D. x = 1 ± √13

Question 3

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

Answer 

Question 4

Solve x² + 4x − 1 = 0 by completing the square. Give the smaller solution to 2 decimal places.

Answer 

Question 5

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

• A. x = −2 ± 2√2
• B. x = −2 ± 8
• C. x = −4 ± 2√2
• D. x = 2 ± 2√2

Question 6

Rewrite x² − 4x + 10 = 0 as (x − 2)² = k. Find k.

Answer 

Question 7

Solve x² − 6x − 21 = 0 by completing the square. Give the smaller solution to 2 decimal places.

Answer 

Question 8

Solve x² − 12x + 28 = 0 by completing the square. Give exact answers.

• A. x = 6 ± √44
• B. x = −6 ± 2√2
• C. x = 6 ± 8
• D. x = 6 ± 2√2

Question 9

Rewrite x² + 8x + 15 = 0 as (x + 4)² = k. Find k.

Answer 

Question 10

Solve x² − 2x − 27 = 0 by completing the square. Give the larger solution to 2 decimal places.

Answer 

Question 11

Solve x² + 6x − 9 = 0 by completing the square. Give exact answers.

• A. x = −3 ± 18
• B. x = 3 ± 3√2
• C. x = −3 ± 3√2
• D. x = −3 ± √27

Question 12

Rewrite x² + 2x + 5 = 0 as (x + 1)² = k. Find k.

Answer 

Question 13

Solve x² − 8x + 11 = 0 by completing the square. Give the smaller solution to 2 decimal places.

Answer 

Question 14

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

• A. x = −6 ± 2√6
• B. x = −6 ± 24
• C. x = 6 ± 2√6
• D. x = −12 ± 2√6

Question 15

Rewrite x² + 4x − 8 = 0 as (x + 2)² = k. Find k.

Answer 

Question 16

Solve x² − 4x − 7 = 0 by completing the square. Give the larger solution to 2 decimal places.

Answer