By assuming that the solution to the equation $x^4 - x - 10 = 0$ lies between $x = 1.8$ and $x = 2$, then the next approximate solution by Regula-falsi method is (Take $f(1.8) = -1.3024$):
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Regula-Falsi uses the formula of a straight line connecting $(a, f(a))$ and $(b, f(b))$. Keep track of the negative signs carefully in the denominator, as subtracting a negative number yields an addition!