Solve the equation x^6 + 26x^3 − 27 = 0

While this equation may look complicated, it's actually much easier than it looks - this equation is called a hidden quadratic. This is because it can be rewritten and solved the same way you would solve a quadratic. This becomes clear when you compare it to how a quadratic looks: a w^2 + b w + c. Since the power of the first term is double the power of the second term and the last term is a constant, it can be identified as a hidden quadratic and using the substitution w = x^3, can be rewritten as one (this will be an equation in terms of w).This can be done as follows: x^6 + 26x^3 -27 = 0 (=>) w^2 + 26w -27 = 0 (=>) (w+27) (w-1) = 0 Here is where we substitute x^3 back in to get the equation in terms of x again! (=>) (x^3+27)(x^3-1) = 0 (=>) x^3 = -27 and x^3 = 1 By cube rooting -27 and 1, we get the solutions x=-3 and x =1