Question

Simplify your answer. Type an exact answer, using radicals and as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.

Answer 1

Start reordering the equation:

`\begin{gathered} 113x^2+1=16x\text{ subtract 16x from both sides} \\ 113x^2+1-16x=16x-16x \\ 113x^2+1-16x=0\text{ reorder the terms} \\ 113x^2-16x+1=0 \end{gathered}`

Use the quadratic formula to find the roots:

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\begin{cases}a=113 \\ b=-16 \\ c=1\end{cases} \\ x=\frac{-(-16)\pm\sqrt[]{(-16)^2-4(113)(1)}}{2(113)} \\ x=\frac{16\pm\sqrt[]{256-452}}{226} \\ x=\frac{16\pm\sqrt[]{-196}}{226}=\frac{16\pm\sqrt[]{196}\cdot\sqrt[]{-1}}{226} \\ x=(16\pm14i)/(226)\text{ simplify numbers} \\ x=(8\pm7i)/(113)\text{ the answers are} \\ x1=(8)/(113)+(7i)/(113)\text{ and }x2=(8)/(113)-(7i)/(113) \end{gathered}`