The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Solve Quadratic Equations by Completing the Square

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

'Solve Quadratic Equations by Completing the Square' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Translate Simple Situations or Procedures into Algebraic Expressions, Formulae or Equations

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

This worksheet is about solving quadratic equations by completing the square.

 

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

 

(Give your answers to 2 dps.)

  • Question 1

Select all the solutions to this equation:

x 2 - 4x - 21 = 0

 

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

Select all the solutions to this equation:

x 2 + 11x + 24 = 0

 

 

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

Select all the solutions to this equation:

x 2 - 16x + 54 = 0

 

 

CORRECT ANSWER
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

 

CORRECT ANSWER
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

 

CORRECT ANSWER
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

 

CORRECT ANSWER
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

 

 

CORRECT ANSWER
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

 

 

CORRECT ANSWER
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

 

 

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

Solve the following  equations:

x 2 + 17x + 29 = 0

 

(Give your answers to 2 dps.)

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

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Start your £1 trial

Start your trial for £1