Question

Evaluate the expression for q = 5: q +8.9

Answer 1

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:

`q=(5)/(q)+8.9`

Now, we can start by multiplying both sides by "q":

`\begin{gathered} q^2=5+8.9q \\ q^2-8.9q-5=0 \end{gathered}`

We have got a quadratic equation and we need to find its zero, so we can use the quadratic formula:

`\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(8.9\pm9.96)/(2) \end{gathered}`

Now, we will have two answers:

`q_1\approx(8.9+9.96)/(2)=(18.86)/(2)=9.43`

And:

`q_2=(8.9-9.96)/(2)=(-1.06)/(2)=-0.53`

So, the solutions for the equation are 9.43 and -0.53.