Answer:
x = ± sqrt(6) + 1
Step-by-step explanation:
[tex]x^2 - 2x = 5[/tex]
First, add half of -2 squared to both sides:
[tex]x^2 - 2x + (-\frac{2}{2})^2 = 5 + (-1)^2[/tex]
[tex]x^2 - 2x + 1 = 5 + 1[/tex]
[tex]x^2 - 2x + 1 = 6[/tex]
Then, factor the perfect square trinomial on the left:
[tex](x - 1)^2 = 6[/tex]
Finally, square root both sides:
[tex]\sqrt{(x - 1)^2} = \sqrt{6}[/tex]
[tex]x - 1 = \sqrt{6}[/tex] or [tex]x - 1 = -\sqrt{6}[/tex]
x = ± sqrt(6) + 1
