Answer:
x = -1 or x = 4
Step-by-step explanation:
[tex]x^2-2x-1=x+3[/tex]
subtract [tex]x[/tex] from both sides:
[tex]\implies x^2-2x-1-x=x+3-x[/tex]
[tex]\implies x^2-3x-1=3[/tex]
subtract 3 from both sides:
[tex]\implies x^2-3x-1-3=3-3[/tex]
[tex]\implies x^2-3x-4=0[/tex]
factor:
[tex]\implies x^2+x-4x-4=0[/tex]
[tex]\implies x(x+1)-4(x+1)=0[/tex]
[tex]\implies (x-4)(x+1)=0[/tex]
Therefore,
[tex]x-4=0 \implies x=4[/tex]
[tex]x+1=0 \implies x=-1[/tex]
