Supposex$^7+5$tan$($x$)+2=0,$ where x in $[$$/4,$ $/4]$

Prove the equation has exactly one real solution on the given interval.

Use Newton's Method to find the root.

If you are dealing with a trigonometric function, make sure your calculator is in radian mode!!!

State your initial guess.

x$0=$

State your computed value for x$1.$

You MUST answer part $($i$)$ before answering this part.

x$1$

State your computed value for x$2.$

x$2$

Continue to use Newton's Method until you find the root accurate to at least $5$ decimal places.

The solution is approximately