$1\mathrm{.}2.$ A reversible chemical reaction

$2A+$BharrC

can be characterized by the equilibrium relationship

$K=\frac{c_c}{c_a^2{c}_b}$

where the nomenclature $c_i$ represents the concentration of constituent $i.$ Suppose that

we define a variable $x$ as representing the number of moles of $C$ that are produced.

Conservation of mass can be used to reformulate the equilibrium relationship as

$K=\frac{(c_{c,0}+x)}{(c_{a,0}-2x{)}^2(c_{b,0}-x)}$

where the subscript $0$ designates the initial concentration of each constituent. If $K=$

$0\mathrm{.}016,c_{a,0}=42,c_{b,0}=28$ and $c_{c,0}=4,$ determine the value of $x.$

$1\mathrm{.}2\mathrm{.}1.$ Used the bisection rule $($create an m $-$file$)$ to find the roots with the initial

guesses of $x_i=0$ and $x_u=20$ and an absolute error of $0\mathrm{.}5\%.$

$[$Hint: simplify the equation$]$ using matlab