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QMMaths

Trial and Improvement

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Answers

    For each equation below, write the next value of x that you would try in the table and find the solution to the equation

  1. x^{2} + x = 72 . What value of x would you try next in the table below?
    x x^{2} + x comment
    5 30 Too low
    11 132 Too high
  2. Find the exact solution for x^{2} + x = 72
  3. 2x^{2} - x = 28 . What value of x would you try next in the table below?
    x 2x^{2} - x comment
    1 1 Too low
    6 66 Too high
  4. Find the exact solution for 2x^{2} - x = 28
  5. x^{3} - 2x = 115 . What value of x would you try next in the table below?
    x x^{3} - 2x comment
    8 496 Too high
    3 21 Too low
  6. Find the exact solution for x^{3} - 2x = 115

    7. Using trial and improvement, find the solution to the following equations to the given number of decimal places

  7. x^{2} - x = 88 (to 1 d.p.)
  8. x + x^{3} = 117 (to 1 d.p.)
  9. x\left( x - 5 \right) = 59 (to 2 d.p.)
  10. 2^{x} = 7 (to 2 d.p.)

    11. The product of two consecutive integers is 210

  11. Calling x the smallest of the two integers, write an equation for x.
  12. Using trial and improvement, find the value of x