The expression q = 5:q +8.9 has no parenthesis, so we will use the Order of Expression next. After parenthesis, we have to evaluate multiplication and division, so the given expression is equivalento of:
[tex]q=\frac{5}{q}+8.9[/tex]Now, we can start by multiplying both sides by "q":
[tex]\begin{gathered} q^2=5+8.9q \\ q^2-8.9q-5=0 \end{gathered}[/tex]We have got a quadratic equation and we need to find its zero, so we can use the quadratic formula:
[tex]\begin{gathered} q=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{8.9\pm\sqrt[]{(-8.9)^2-4\cdot1\cdot(-5)}}{2\cdot1} \\ q=\frac{8.9\pm\sqrt[]{79.21+20}}{2}=\frac{8.9\pm\sqrt[]{99.21}}{2} \\ q\approx\frac{8.9\pm9.96}{2} \end{gathered}[/tex]Now, we will have two answers:
[tex]q_1\approx\frac{8.9+9.96}{2}=\frac{18.86}{2}=9.43[/tex]And:
[tex]q_2=\frac{8.9-9.96}{2}=\frac{-1.06}{2}=-0.53[/tex]So, the solutions for the equation are 9.43 and -0.53.
