Answer:
B. [tex]x=-7\text{ and }x=-1[/tex].
Step-by-step explanation:
We have been given an equation [tex]x^2+8x+7=0[/tex]. We are asked to find the solutions of our given equation.
We will factor our given equation by splitting the middle term as shown below:
[tex]x^2+7x+x+7=0[/tex]
[tex]x(x+7)+1(x+7)=0[/tex]
[tex](x+7)(x+1)=0[/tex]
Using zero product property, we will equate both factors of our given equation with 0 as:
[tex](x+7)=0\text{ (or) }(x+1)=0[/tex]
[tex]x+7=0\text{ (or) }x+1=0[/tex]
[tex]x=-7\text{ (or) }x=-1[/tex]
Therefore, the solutions for our given equation are [tex]x=-7\text{ and }x=-1[/tex] and option B is the correct choice.
