solve the following

Question

Solve 5𝑥 3 + 6(1−𝑥) 7 = 65

Answer 1

15x-42x+42=65

27x=-23

x=-23/27

Answer 2

5x^3 + 6(1-x)7 = 65

5x^3 -42x - 23 = 0

x = about 3.1407956

x also has two imaginary solutions

try graphing it on an online graphing website, such as Desmos. where it intersects the x axis is the soluiton.

or an online equation solver. There's only one real solution.

Use Decartes' rule of signs to determine there's a maximum one positive real solution

two possible negative real solutions, but it turns out there are no negative real solutions

cubic equations are not easy to solve

unless you meant 5x^3 +6(1-x)^7 = 65,

then it's far more complicated, with 7 possible solutions

x=about -0.40295378

with likely 6 imaginary solutions. They come in conjugate pairs

there are as many solutions as the highest degree. IF it's even, they could all be imaginary. If it's odd, there's at least on real solution