How do you figure out x?
-0.00996 - 0.4012x - 3.9712x^2 + 1.08x^3 = 0
I would graph
y=-0.00996 - 0.4012x - 3.9712x^2 + 1.08x^3
and see where it crosses the y=0 axis, those are the solution points. You may have to adjust your graphing calculator x scale a few times to see the solution points.
I can't get the right value. I know the answer is supposed to be 0.04648 but I'm not getting it from the graph.
To figure out the value of x in the equation -0.00996 - 0.4012x - 3.9712x^2 + 1.08x^3 = 0, you can use various methods such as factoring, graphing, or numerical methods like the Newton-Raphson method. Let's explore the most common method, which is solving the equation using numerical approximation.
One common numerical method to solve equations like this is called the Newton-Raphson method. It is an iterative method that starts with an initial guess and improves the approximation with each iteration until it converges to the solution.
Here's an outline of how to apply the Newton-Raphson method to find the roots of your equation:
1. Rewrite the equation in the form of f(x) = 0. In this case, the equation becomes f(x) = -0.00996 - 0.4012x - 3.9712x^2 + 1.08x^3 = 0.
2. Compute the derivative of f(x) with respect to x. Let's call it f'(x).
3. Choose an initial guess, let's say x0.
4. Use the following formula to iteratively approximate the root:
x(n+1) = x(n) - f(x(n))/f'(x(n))
Repeat this step until the approximation converges to the desired accuracy.
5. Continue iterating until you reach the desired level of accuracy or convergence.
It's important to note that the Newton-Raphson method may not always work for every equation or initial guess. In some cases, the method may fail to converge, or it may converge to a local minimum or maximum instead of the root you are looking for. In those cases, you may need to try a different method or adjust your initial guess.
Alternatively, you can use numerical solvers or software, such as mathematical software packages like MATLAB, Python with libraries like NumPy, or online tools, to find the roots of your equation accurately.
Remember to check your answer by substituting the obtained value of x back into the original equation to ensure it satisfies the equation.