Question

ASAP WILL MARK BRAINLYEST solve these equation by completing the square:

Answer 1

$(*)\qquad(a\pm b)^2=a^2\pm2ab+b^2\\-------------------------------------\\12.\\r^2-6r=0\\\\r^2-2\cdot r\cdot3=0\ \ \ \ \ |+3^2\\\\\underbrace{r^2-2\cdot r\cdot3+3^2}_{(*)}=3^2\\\\(r-3)^2=9\to r-3=\pm\sqrt9\\\\r-3=-3\ \vee\ r-3=3\ \ \ \ |+3\\\\\boxed{r=0\ \vee\ r=6}\\\\13.\\t^2-12t+20=0\ \ \ \ |-20\\\\t^2-2\cdot t\cdot6=-20\ \ \ \ \ |+6^2\\\\\underbrace{t^2-2\cdot t\cdot6+6^2}_{(*)}=-20+36\\\\(t-6)^2=16\to t-6=\pm\sqrt{16}\\\\t-6=-4\ \vee\ t-6=4\ \ \ \ |+6\\\\t=2\ \vee\ t=10$

$14.\\c^2+4c-7=0\ \ \ \ \ \ |+7\\\\c^2+2\cdot c\cdot2=7\ \ \ \ \ |+2^2\\\\\underbrace{c^2+2\cdot c\cdot2+2^2}_{(*)}=7+4\\\\(c+2)^2=11\to c+2=\pm\sqrt{11}\ \ \ \ \ |-2\\\\c=-2-\sqrt{11}\ \vee\ c=-2+\sqrt{11}$