X^5 -x^4 -7x = 4
Solve by graphing

  x ∈ {-1.18357720838, -0.601342529307, 2.04583491964, 0.369542409021 ±i√2.61051577416}

Step-by-step explanation:

A graphing calculator is useful for finding approximations of real roots and for iterating those roots to full calculator precision. It can also show the roots of any remaining quadratic factors.

Here, the solutions are listed above.

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The iteration method used here is Newton's method. The iteration function is ...

  g(x) = x -f(x)/f'(x) . . . . g(x) is the next iteration of x; f'(x) is the derivative of f(x)

It will converge rapidly on a solution using the graph zeros as starting values.

The graph shows the quadratic result of factoring the real roots from the original polynomial. It has only complex roots, found easily from the coordinates of the vertex.