Solve the Problem $- 4 \mathrm { x } ^ { 2 } - 2 \mathrm { x } + 1 = 0$

Essay

Solve the problem.
-Use Newton's method to estimate the solutions of the equation $- 4 \mathrm { x } ^ { 2 } - 2 \mathrm { x } + 1 = 0$ . Start with $\mathrm { x } _ { 1 } = 0.5$ for the right-hand solution and with $\mathrm { x } _ { 0 } = - 2$ for the solution on the left. Then, in each case find $\mathrm { x } _ { 2 }$ .