Question

Please help me solve x^2-2x-1=x+3

Answer 1

x = -1 or x = 4

Explanation:

`x^2-2x-1=x+3`

subtract
`x` from both sides:

`\implies x^2-2x-1-x=x+3-x`

`\implies x^2-3x-1=3`

subtract 3 from both sides:

`\implies x^2-3x-1-3=3-3`

`\implies x^2-3x-4=0`

factor:

`\implies x^2+x-4x-4=0`

`\implies x(x+1)-4(x+1)=0`

`\implies (x-4)(x+1)=0`

Therefore,

`x-4=0 \implies x=4`

`x+1=0 \implies x=-1`