... out were the formula crosses the x-axis, which was 0.7 and 0.8. I then expanded this to one more decimal place and found the point where it crosses, to be between 0.71 and 0.72. I expand this again twice more to find the 3rd and 4th decimal places which are (0.716 & 0.717) and (0.7169 and 0.717) respectively. 0.7 -0.148 0.71 -0.06057 0.72 0.026112 0.73 0.111998 0.74 0.197056 0.716 -0.00847 0.75 0.28125 0.7161 -0.0076 0.76 0.364544 0.7162 -0.00673 0.77 0.446902 0.7163 -0.00587 0.78 0.528288 0.7164 -0.005 0.79 0.608666 0.7165 -0.00414 0.8 0.688 0.7166 -0.00327 0.7167 -0.00241 0.7168 -0.00154 0.71 -0.06057 0.7169 -0.00068 0.711 -0.05186 0.717 0.00019 0.712 -0.04317 0.713 -0.03448 0.714 -0.0258 0.71695 -0.00024 0.715 -0.01713 0.71705 0.000623 0.716 -0.00847 0.717 0.00019 0.718 0.008839 0.719 0.017479 0.72 0.026112 0.71695 -0.00024 0.71705 0.000623 Thus proves that the root lies no greater nor less than 0.00005 away from 0.717. It also shows it's correct by the change in sign. Failure of "change of sign" Failure will occur if: * The curve touches the x-axis. * There are several roots close together * There is a discontinuity in f(x) I am going to use decimal search to find the roots of another equation -2x2-3x-1.12 I cannot use decimal search for this equation as it doesn't cross the x-axis. There are some cases where the roots cannot always be found. Reasons for this could be if the ...

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