 # Solve Complex Equations Using Trial and Improvement

In this worksheet, students practise using trial and improvement to solve complex equations. Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Understand Expressions, Equations, Inequalities, Terms and Factors

Difficulty level:   ### QUESTION 1 of 10

In this worksheet, you must use trial and improvement to solve equations.

Example

Solve a2 = 54 giving the answer to 1 decimal place.

Try a value you think will be close to the answer.

 a = a2 = 7 49 This is too small. Try a bigger value. 8 64 This is too big. Try between 7 and 8. 7.5 56.25 Too big. Try a smaller number. 7.3 53.29 Too small. 7.4 54.76 Too big. 7.35 54.02 Too big.

The value of a is closer to 7.3 than 7.4

Answer to 1 decimal place is a = 7.3

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

x2 = 77   starting with x = 9

8.6

8.7

8.8

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

x2 + 4x = 75   starting with x = 7

7.1

7

6.9

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

8x2 + 4x = 75    starting with x = 3

3.2

2.8

2.9

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

x2 + x = 13    starting with x = 3

3.2

3.0

3.1

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

6x3 - 6x = 111    starting with x = 3

3.2

2.8

3.1

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

9x3 - 3x  = 113    starting with x = 2

2.4

2.8

2.6

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

x3 + 5x  = 22   starting with x = 2

2.2

2.0

2.1

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

x3 + x  = 538   starting with x = 8

8.1

8.2

8.3

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

8x2 + 3x - 11  = 691   starting with x = 9

9.1

9.2

9.3

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

4x2 + 7x - 6  = 348   starting with x = 9

9.1

8.9

8.6

• Question 1

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

x2 = 77   starting with x = 9

8.8
• Question 2

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

x2 + 4x = 75   starting with x = 7

6.9
• Question 3

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

8x2 + 4x = 75    starting with x = 3

2.8
• Question 4

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

x2 + x = 13    starting with x = 3

3.1
• Question 5

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

6x3 - 6x = 111    starting with x = 3

2.8
• Question 6

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

9x3 - 3x  = 113    starting with x = 2

2.4
• Question 7

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

x3 + 5x  = 22   starting with x = 2

2.2
• Question 8

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

x3 + x  = 538   starting with x = 8

8.1
• Question 9

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

8x2 + 3x - 11  = 691   starting with x = 9

9.2
• Question 10

Use trial and improvement to solve this equation for x to 1 decimal place, starting with the given value.

4x2 + 7x - 6  = 348   starting with x = 9

8.6
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