Question

Find all the roots x^2-2x-4​

Answer 1

`\large\boxed{x=1-\sqrt5\ \vee\ x=1+\sqrt5}`

Explanation:

`x^2-2x-4=0\qquad\text{add 4 to both sides}\\\\x^2-2x=4\\\\x^2-2(x)(1)=4\qquad\text{add}\ 1^2\ \text{to both sides}\\\\x^2-2(x)(1)+1^2=4+1^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-1)^2=4+1\\\\(x-1)^2=5\to x-1=\pm\sqrt5\qquad\text{add 1 to both sides}\\\\\boxed{x=1-\sqrt5}\ \vee\ \boxed{x=1+\sqrt5}`