Question

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

Answer 1

Answer:

$x_{1}=-1\\ x_{2}=1\\ x_{3}=-7$

Step-by-step 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.