What value of y satisfies the equation y3+14=512
$$y^3=512-14\\
y^3=498$$
$$y\approx 7.926$$
$${{\mathtt{y}}}^{{\mathtt{3}}} = {\mathtt{498}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{y}} = {\frac{\left({\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{{\mathtt{498}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{{\mathtt{498}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}{{\mathtt{2}}}}\\
{\mathtt{y}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{{\mathtt{498}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{{\mathtt{498}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}{{\mathtt{2}}}}\\
{\mathtt{y}} = {{\mathtt{498}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{y}} = {\mathtt{\,-\,}}{\mathtt{3.963\: \!204\: \!222\: \!244\: \!851\: \!5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6.864\: \!471\: \!073\: \!704\: \!028\: \!8}}{i}\\
{\mathtt{y}} = {\mathtt{\,-\,}}\left({\mathtt{3.963\: \!204\: \!222\: \!244\: \!851\: \!5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6.864\: \!471\: \!073\: \!704\: \!028\: \!8}}{i}\right)\\
{\mathtt{y}} = {\mathtt{7.926\: \!408\: \!444\: \!489\: \!703}}\\
\end{array} \right\}$$
6.4 - 2x - 6.63x = 610.5
Combine the x-terms:
6.4 - 8.63x = 610.5
Subtract 6.4 from both sides:
- 8.63x = 604.1
Divide both sides by -8.63:
x = -71.66 (approximately)
What value of y satisfies the equation y3+14=512
$$y^3=512-14\\
y^3=498$$
$$y\approx 7.926$$
$${{\mathtt{y}}}^{{\mathtt{3}}} = {\mathtt{498}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{y}} = {\frac{\left({\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{{\mathtt{498}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{{\mathtt{498}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}{{\mathtt{2}}}}\\
{\mathtt{y}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{{\mathtt{498}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{{\mathtt{498}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}{{\mathtt{2}}}}\\
{\mathtt{y}} = {{\mathtt{498}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{y}} = {\mathtt{\,-\,}}{\mathtt{3.963\: \!204\: \!222\: \!244\: \!851\: \!5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6.864\: \!471\: \!073\: \!704\: \!028\: \!8}}{i}\\
{\mathtt{y}} = {\mathtt{\,-\,}}\left({\mathtt{3.963\: \!204\: \!222\: \!244\: \!851\: \!5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6.864\: \!471\: \!073\: \!704\: \!028\: \!8}}{i}\right)\\
{\mathtt{y}} = {\mathtt{7.926\: \!408\: \!444\: \!489\: \!703}}\\
\end{array} \right\}$$