# Solve Quadratic Equations by Completing the Square

In this worksheet, students solve quadratic equations by completing the square.

Key stage:  KS 4

Curriculum topic:  Algebra

Difficulty level:

### QUESTION 1 of 10

 Example Solve by completing the square, x2-10x+17=0. Give your answers to 3 sig. figs.

 Solution (x-5)2-25+17=0 (x-5)2=8 (rearranging) x-5 = ±√8 x = 5+√8  or  5-√8 x = 7.83 or 2.17 (to 3 sf.)

 Remember to complete the square on the expression x2+bx+c write (x+b/2)2 - b2/4 +c and proceed as above.

﻿Select all the solutions to this equation:

x 2 - 4x - 21 = 0

-3

7

3

-7

Select all the solutions to this equation:

x 2 + 11x + 24 = 0

-3

3

8

-8

Select all the solutions to this equation:

x 2 - 16x + 54 = 0

11.2

-4.84

4.84

-11.2

Select all the solutions to this equation:

x 2 - 11x + 7 = 0

10.3

12.3

0.678

0.741

Select all the solutions to this equation:

x 2 - 20x + 86 = 0

5.45

6.26

13.7

12.4

Select all the solutions to this equation:

x 2 - 12x + 25 = 0

9.31

2.69

2.68

9.32

Select all the solutions to this equation:

x 2 - 19x + 76 = 0

13.3

13.2

5.27

5.73

Select all the solutions to this equation:

x 2 - 9x + 19 = 0

-5.62

5.62

3.38

-3.38

Select all the solutions to this equation:

x 2 - 7x + 12.25 = 0

3.5

-3.5

-7

7

Solve the following  equations:

x 2 + 17x + 29 = 0

• Question 1

﻿Select all the solutions to this equation:

x 2 - 4x - 21 = 0

-3
7
EDDIE SAYS
(x - 2)² - 25 = 0
• Question 2

Select all the solutions to this equation:

x 2 + 11x + 24 = 0

-3
-8
EDDIE SAYS
(x + 5½)² - 6¼ = 0
• Question 3

Select all the solutions to this equation:

x 2 - 16x + 54 = 0

11.2
4.84
EDDIE SAYS
(x - 8)² - 10 = 0
• Question 4

Select all the solutions to this equation:

x 2 - 11x + 7 = 0

10.3
0.678
EDDIE SAYS
(x - 5½)² - 23¼ = 0
• Question 5

Select all the solutions to this equation:

x 2 - 20x + 86 = 0

6.26
13.7
EDDIE SAYS
(x - 10)² - 14 = 0
• Question 6

Select all the solutions to this equation:

x 2 - 12x + 25 = 0

2.68
9.32
EDDIE SAYS
(x - 6)² - 11 = 0
• Question 7

Select all the solutions to this equation:

x 2 - 19x + 76 = 0

13.3
5.73
EDDIE SAYS
(x - 9.5)² - 14.25 = 0
• Question 8

Select all the solutions to this equation:

x 2 - 9x + 19 = 0

5.62
3.38
EDDIE SAYS
(x - 4.5)² - 1.25 = 0
• Question 9

Select all the solutions to this equation:

x 2 - 7x + 12.25 = 0

3.5
EDDIE SAYS
(x - 3.5)² = 0
Only one solution
• Question 10

Solve the following  equations:

x 2 + 17x + 29 = 0

-1.92
-15.08
EDDIE SAYS
(x + 8.5)² - 43.25 = 0
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