Solve Complex Equations Using Trial and Improvemen...
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  • Introduction
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In this worksheet, you must use trial and improvement to solve equations.

 

Example

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

 

Answer


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

  • Question 1
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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

  • Question 2
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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

  • Question 3
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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

  • Question 4
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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

  • Question 5
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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

  • Question 6
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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

  • Question 7
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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

  • Question 8
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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

  • Question 9
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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

  • Question 10
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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

Progress