Question

Solve the equation. 42 = d^2 – 22 d = and d =

Answer 1

`\begin{gathered} 42=d^2-22d \\ d^2-22d-44=0 \\ \\ \text{ For equations like } \\ ad^2+bd+c=0,\text{ we have that the solution is} \\ \\ d=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ \text{ Thus for the equation} \\ \\ d^2-22d-44=0 \\ \\ \text{The solutions are} \\ \\ d=\frac{-(-22)\pm\sqrt[]{(-22)^2-4(1)(-44)}}{2(1)} \\ \\ d=\frac{22\pm\sqrt[]{484+176}}{2} \\ \\ d=\frac{22\pm\sqrt[]{660}}{2} \\ \\ d=\frac{22\pm2\sqrt[]{165}}{2} \\ \\ d=11\pm\sqrt[]{165} \end{gathered}`