Answer:
[tex]x_{1}=-1\\ x_{2}=1\\ x_{3}=-7[/tex]
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:
[tex]x^{2} (x+7)-x-7=0\\x^{2} (x+7) = (x+7)[/tex]
The (x+7) term can be crossed out on both sides and then for this equation to be true, there are two possibilities:
Either
[tex]x^{2} =1\\x_{1} = 1\\x_{2} = -1[/tex]
or
[tex](x+7) = 0\\x_{3} = -7[/tex]
Therefore, the solutions to this equation are -1, 1 or -7.
