Answer:
C. [tex]x=-9 \textsf{ and }x=1[/tex]
Step-by-step explanation:
[tex](x+4)^2=25[/tex]
[tex](x+4)(x+4)=25[/tex]
expand the brackets:
[tex]x^2+8x+16=25[/tex]
subtract 25 from both sides:
[tex]x^2+8x-9=0[/tex]
factor:
[tex]x^2+9x-x-9=0[/tex]
[tex]x(x+9)-1(x+9)=0[/tex]
[tex](x-1)(x+9)=0[/tex]
solve for x:
[tex]x-1=0 \implies x=1[/tex]
[tex]x+9=0 \implies x=-9[/tex]
