Solving Nonlinear Equations by Factoring

Solve for x: x⁴ - 21x² - 35 = 65

Example

So, there are four solutions: -2i, +2i, -5, and +5.

The equation x⁴ - 21x² - 35 = 65 written in standard form is x⁴ - 21x² - 100 = 0. The graph of the corresponding function, f(x) = x⁴ - 21x² - 100 is shown.

The graph crosses the x-axis at only two locations, x = -5 and x = 5. This is because these are the only real number solutions.