Question

In Problems 81–92, use a graphing utility to solve each equation. Express the solution(s) rounded to two decimal places.

$x^2-2\sin \left(2x\right)=3x$

Short answer

The solution set is$\left\{0,2.15\right\}$.

Step-by-step solution

Step 1. Given Information

In the given problems we have to use a graphing utility to solve each equation and express the solution(s) rounded to two decimal places.

$x^2-2\sin \left(2x\right)=3x$

Step 2. This type of trigonometric equation cannot be solved by previous methods. A graphing utility, though, can be used here.

Each solution of this equation is the x-coordinate of a point of intersection of the graphs of $Y_1=x^2-2\sin \left(2x\right)\mathrm{and}{\mathrm{Y}}_2=3x$.

Step 3. The graph of the given equation is

Step 4. There are three points of intersection; the x-coordinates are the solutions that we seek.

Using INTERSECT, we find

$x=0x=2.15$

The solution set is$\left\{0,2.15\right\}$.