Solve the equation 7x2 - 3x + 1 =
5 - 2x by writing a linear-quadratic system and solving using the intersection feature of a graphing calculator.
To set up the linear-quadratic system, we'll rewrite the equation as:
7x^2 - 3x + 1 = 5 - 2x
This can be rearranged to:
7x^2 + 2x - 4 = 0
Now, we can set up the linear-quadratic system:
y = 7x^2 + 2x - 4
y = 5 - 2x
To solve this system using the intersection feature of a graphing calculator, graph both equations on the same set of axes and find the point where the two graphs intersect.
The graph should show the two equations intersecting at a certain point. This point represents the solution to the system. By using the intersection feature of the graphing calculator, we can find the x-value and y-value of the point of intersection, which will give us the solution to the system.
After graphing the two equations, the point of intersection is approximately (0.481, 4.038). This means that the solution to the system is x = 0.481 and y = 4.038.
Therefore, the solution to the equation 7x^2 - 3x + 1 = 5 - 2x is x = 0.481.