Solve the given exponential equation. Round answer to three decimal places.
-$$2 ^ { x } - 4 x + 2 = 0$$
A) $\{ 1.000 \}$
B) $\{ 12.639 \}$
C) $\{ 3.660 \}$
D) $\{ 1.000,3.660 \}$

Question

Quizplus · Accepted Answer

This equation cannot be solved algebraically using standard methods due to the presence of both $x$ in the exponent and $x$ as a linear term. Therefore, numerical methods or graphing calculators are typically used to find the solutions. By plotting the function $f(x) = 2^x - 4x + 2$ and finding its intersections with the x-axis, we can identify the approximate solutions. The correct answers, rounded to three decimal places, are $x = 1.000$ and $x = 3.660$, which correspond to the points where the function crosses the x-axis.

Solve the Given Exponential Equation 2x−4x+2=02 ^ { x } - 4 x + 2 = 02x−4x+2=0

Solve the Given Exponential Equation $2 ^ { x } - 4 x + 2 = 0$