Question

Solve the following equation, and explain your solution method.x³+7x²-x-7=0

Answer 1

`x_(1)=-1\\ x_(2)=1\\ x_(3)=-7`

Explanation:

The easiest way to solve this equation is to first find and highlight a common factor between two terms. In this case, x^2 can be factored to rewrite the equation as follows:

`x^(2) (x+7)-x-7=0\\x^(2) (x+7) = (x+7)`

The (x+7) term can be crossed out on both sides and then for this equation to be true, there are two possibilities:

Either

`x^(2) =1\\x_(1) = 1\\x_(2) = -1`

or

`(x+7) = 0\\x_(3) = -7`

Therefore, the solutions to this equation are -1, 1 or -7.