Solve x3 plus 7x equals 8x2?

Answer 1

x3 + 7x = 8x2

x3 + 7x - 8x2 = 0 [subtract 8x2 from both sides]

x(x2 + 7 - 8x) = 0 [factor out x]

x(x-1)(x-7) = 0 [factor]

Since the product of the three factors x, x-1, and x-7 equals zero, any of the three expressions could equal zero:

x = 0

x - 1 = 0, x = 1

x - 7 = 0, x = 7

Therefore, there are three solutions to the equation x3 + 7x = 8x2:

1. x = 0
2. x = 1
3. x = 7

Or, in set notation: x = {0,1,7}