Answer :
[tex]1.\ k^2=76\\\\k=\pm\sqrt{76}\\\\k=\pm\sqrt{4\cdot19}\\\\k=\pm2\sqrt{19}\\-------------\\2.\ k^2=16\\\\k=\pm\sqrt{16}\\\\k=\pm4\\-------------\\[/tex]
[tex]3.\ x^2=21\\\\x=\pm\sqrt{21}\\-------------\\4.\ a^2=40\\\\a=\pm\sqrt{40}\\\\a=\pm\sqrt{4\cdot10}\\\\a=\pm2\sqrt{10}\\-------------\\5.\ x^2+8=28\ \ \ /-8\\\\x^2=20\\\\x=\pm\sqrt{20}\\\\x=\pm\sqrt{4\cdot5}\\\\x=\pm2\sqrt5\\-------------\\[/tex]
[tex]6.\ 2n^2=-144\ \ \ \ /:2\\\\n^2=-72-no\ real\ solutions\\-------------\\7.\ -6m^2=-414\ \ \ \ /:(-6)\\\\m^2=69\\\\m=\pm\sqrt{69}\\-------------\\8.\ 7x^2=-21\ \ \ \ /:(-7)\\\\x^2=-3-no\ real\ solutions\\-------------\\[/tex]
[tex]9.\ m^2+7=88\ \ \ \ /-7\\\\m^2=88-7\\\\m^2=81\\\\m=\pm\sqrt{81}\\\\m=\pm9\\-------------\\10.\ -5x^2=-500\ \ \ \ /:(_5)\\\\x^2=100\\\\x=\pm\sqrt{100}\\\\x=\pm10\\-------------\\[/tex]
[tex]11.\ -7n^2=-448\ \ \ \ /:(-7)\\\\n^2=64\\\\n=\pm\sqrt{64}\\\\n=\pm8\\-------------\\12.\ -2k^2=-162\ \ \ \ /:(-2)\\\\k^2=81\\\\k=\pm\sqrt{81}\\\\k=\pm9\\-------------\\[/tex]
[tex]13.\ x^2-5=73\ \ \ \ /+5\\\\x^2=78\\\\x=\pm\sqrt{78}\\-------------\\14.\ 16n^2=49\ \ \ \ /:16\\\\n^2=\frac{49}{16}\\\\n=\pm\sqrt\frac{49}{16}\\\\n=\pm\frac{\sqrt{49}}{\sqrt{16}}\\\\n=\pm\frac{7}{4}[/tex]
[tex]3.\ x^2=21\\\\x=\pm\sqrt{21}\\-------------\\4.\ a^2=40\\\\a=\pm\sqrt{40}\\\\a=\pm\sqrt{4\cdot10}\\\\a=\pm2\sqrt{10}\\-------------\\5.\ x^2+8=28\ \ \ /-8\\\\x^2=20\\\\x=\pm\sqrt{20}\\\\x=\pm\sqrt{4\cdot5}\\\\x=\pm2\sqrt5\\-------------\\[/tex]
[tex]6.\ 2n^2=-144\ \ \ \ /:2\\\\n^2=-72-no\ real\ solutions\\-------------\\7.\ -6m^2=-414\ \ \ \ /:(-6)\\\\m^2=69\\\\m=\pm\sqrt{69}\\-------------\\8.\ 7x^2=-21\ \ \ \ /:(-7)\\\\x^2=-3-no\ real\ solutions\\-------------\\[/tex]
[tex]9.\ m^2+7=88\ \ \ \ /-7\\\\m^2=88-7\\\\m^2=81\\\\m=\pm\sqrt{81}\\\\m=\pm9\\-------------\\10.\ -5x^2=-500\ \ \ \ /:(_5)\\\\x^2=100\\\\x=\pm\sqrt{100}\\\\x=\pm10\\-------------\\[/tex]
[tex]11.\ -7n^2=-448\ \ \ \ /:(-7)\\\\n^2=64\\\\n=\pm\sqrt{64}\\\\n=\pm8\\-------------\\12.\ -2k^2=-162\ \ \ \ /:(-2)\\\\k^2=81\\\\k=\pm\sqrt{81}\\\\k=\pm9\\-------------\\[/tex]
[tex]13.\ x^2-5=73\ \ \ \ /+5\\\\x^2=78\\\\x=\pm\sqrt{78}\\-------------\\14.\ 16n^2=49\ \ \ \ /:16\\\\n^2=\frac{49}{16}\\\\n=\pm\sqrt\frac{49}{16}\\\\n=\pm\frac{\sqrt{49}}{\sqrt{16}}\\\\n=\pm\frac{7}{4}[/tex]
