What are the steps for solving this?

Directions Use the quadratic formula to solve the equation in the interval [0,2PI). Then use a graphing utility to approximate the angle x.

4cos^2x-4cosx-1=0

thanks.

quadratic equation?

cosx= (4+-sqrt(16+4))/8

graph y=4cos^2 x - 4cosx + 1 and note where it crosses the y=0 axis.

To solve the given equation using the quadratic formula and approximate the angle x using a graphing utility, follow these steps:

Step 1: Identify the quadratic equation in standard form.
The given equation is: 4cos^2(x) - 4cos(x) - 1 = 0. Notice that the equation is in the form ax^2 + bx + c = 0, where a = 4, b = -4, and c = -1.

Step 2: Determine the values of a, b, and c.
From step 1, we've obtained a = 4, b = -4, and c = -1.

Step 3: Apply the quadratic formula to find the solutions for x.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula: x = (-b ± √(b^2 - 4ac)) / (2a).
In this case, substitute the values of a, b, and c into the quadratic formula: x = (-(-4) ± √((-4)^2 - 4(4)(-1))) / (2(4)).
Simplifying this expression gives you: x = (4 ± √(16 + 16)) / 8.

Step 4: Simplify the expression for x.
Simplifying the expression further, you get: x = (4 ± √(32)) / 8.
x = (4 ± √(16 * 2)) / 8.
x = (4 ± 4√2) / 8.
x = 1/2 ± (1/2)√2.
Hence, the two solutions for x are: x = 1/2 + (1/2)√2, and x = 1/2 - (1/2)√2.

Step 5: Calculate the approximate values for x using a graphing utility.
To approximate the values of x using a graphing utility, you can plot the equation and observe where it intersects the x-axis within the given interval [0, 2π). This will provide an estimate for the values of x.

By following these steps, you have both solved the equation using the quadratic formula and approximated the angle x using a graphing utility.