Final answer:
To solve the equation x³ − 16x = x² − 16, we need to rearrange it to set it to zero and then attempt factoring or apply numerical methods, as it does not factor easily.
Step-by-step explanation:
To solve the equation x³ − 16x = x² − 16, we first need to rearrange it to set the equation to zero. Subtract x² and add 16 to both sides to get x³ - x² - 16x + 16 = 0. Now, we look for common factors or patterns that might help us factor the equation.
Unfortunately, this equation does not factor neatly into easily recognizable binomials or trinomials. Thus, we either need to use more advanced factoring techniques, such as synthetic division or the Rational Root Theorem, or we need to resort to numerical methods such as the Newton-Raphson method or graphing to find approximations of the roots.
If we use the quadratic formula to solve for other types of quadratic equations like x² + bx + c = 0, we simply substitute the coefficients into the formula and solve for x.