Question

What are the solutions to the equation x- 8x = 10?1) 4 102) 4-263) 41104) 4+ 26

Answer 1

First, let's equal the expression to zero:

`\begin{gathered} x^2-8x=10 \\ \rightarrow x^2-8x-10=0 \end{gathered}`

Now, let's use the general formula for quadratic equations:

`\begin{gathered} \text{For} \\ ax^2+bx+c=0 \\ \\ \rightarrow x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}`

This way,

`\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(-10)}}{2(1)} \\ \\ \rightarrow x=\frac{8\pm\sqrt[]{64+40}}{2} \\ \\ \rightarrow x=\frac{8\pm\sqrt[]{104}}{2} \\ \\ \rightarrow x=\frac{8\pm2\text{ }\sqrt[]{26}}{2} \\ \\ \Rightarrow x=4\pm\sqrt[]{26} \end{gathered}`

Answer: Option 2