Question

Use a graphing utility to solve each equation. Express your answer rounded to two decimal places.

$e^{2x}=x+2$

Short answer

The solutions of the given equation are $-1.98$and $0.45$.

Step-by-step solution

Step 1. Given information.

The given equation is:

$e^{2x}=x+2$

Step 2. Determine the solution by the graphing utility.

Plot the graphs of $y_1=e^{2x}$ and$y_2=x+2$ on a coordinate plane. The x-coordinate of the intersection point is the solution of the given equation.

The graphs intersect each other at $x\approx -1.981$ and $x\approx 0.448$. After rounding the value to two decimal places$x\approx -1.98$ and $x\approx 0.45$.

Step 3. Conclusion.

The solutions of the given equation are $-1.98$and $0.45$.