(x - 5)² = x² - 2*5*x + 5² = x² - 10x + 25
We have:
x² - 10x = -12
Adding 25 at both sides of the equal sign
x² - 10x + 25 = -12 + 25
(x - 5)² = 13
[tex]x-5=\sqrt[]{13}[/tex]The square root of 13 has two solutions, one positive and one negative, then:
[tex]\begin{gathered} x-5=\sqrt[]{13} \\ x=\sqrt[]{13}+5 \\ or \\ x-5=-\sqrt[]{13} \\ x=-\sqrt[]{13}+5 \end{gathered}[/tex]