Question

Solve each equation by completing the square. If necessary, round to the nearest hundredth.

19. X²-18x=19
20. 4 a²+8a-20=0

Answer 1

$x^2-18x=19\\\\x^2-2x\cdot9+9^2-9^2=19\\\\(x-9)^2-81=19\\\\(x-9)^2=19+81\\\\(x-9)^2=100\iff x-9=\pm\sqrt{100}\\\\x-9=-10\ \vee\ x-9=10\\\\x=-10+9\ \vee\ x=10+9\\\\x=-1\ \vee\ x=19$



$4a^2+8a-20=0\ \ \ \ /:4\\\\a^2+2a-5=0\\\\a^2+2a\cdot1+1^2-1^2=5\\\\(a+1)^2-1=5\\\\(a+1)^2=5+1\\\\(a+1)^2=6\iff a+1=\pm\sqrt6\\\\a=-\sqrt6-1\ \vee\ a=\sqrt6-1\\\\a\approx-3.45\ \vee\ a=\approx1.45$