Answer
The solution is $x= 2.821$
Work Step by Step
Given \begin{equation}
3.5 \sqrt{1.7 x+6}+2.8=14.3.
\end{equation} Start by rearranging the equation and squaring both sides of the equation to eliminate the radical sign and solve for $x$. \begin{equation}
\begin{aligned}
3.5 \sqrt{1.7 x+6}+2.8&=14.3 \\3.5 \sqrt{1.7 x+6}&=11.5\\ \left( 3.5 \sqrt{1.7 x+6} \right)^2&= \left( 11.5 \right)^2\\12.25\cdot (1.7 x+6)& = 132.25\\ 20.825x+73.5& = 132.25\\ x& =\frac{132.25-73.5}{20.825}\\&\approx 2.821128.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
3.5 \sqrt{1.7 \cdot(2.821128)+6}+2.8 & \stackrel{?}{=} 14.3 \\ 14.3&\approx14.3\checkmark.\end{aligned}
\end{equation} The solution is $x\approx2.821$.
