Respuesta:
1) [tex]-3[/tex]
2) [tex]x=3,\:x=-3[/tex]
3) [tex]x=\sqrt{\frac{7}{2}},\:x=-\sqrt{\frac{7}{2}}[/tex]
4) [tex]x=i\sqrt{\frac{5}{2}}+4,\:x=-i\sqrt{\frac{5}{2}}+4[/tex]
Explicación paso a paso:
1) Procedimiento :
[tex]5x^2=45\\\\\frac{5x^2}{5}=\frac{45}{5}\\\\x^2=9\\\\x=\sqrt{9},\:x=-\sqrt{9}\\\\\sqrt{9}\\\\=\sqrt{3^2}\\\\=3\\\\-\sqrt{9}\\\\=\sqrt{3^2}\\\\=3\\\\=-3\\\\[/tex]
2) Procedimiento :
[tex]\frac{2}{3}x^2+14=20\\\\\frac{2}{3}x^2+14-14=20-14\\\\\frac{2}{3}x^2=6\\\\3\cdot \frac{2}{3}x^2=6\cdot \:3\\\\2x^2=18\\\\\frac{2x^2}{2}=\frac{18}{2}\\\\x^2=9\\\\x=\sqrt{9},\:x=-\sqrt{9}\\\\x=3,\:x=-3[/tex]
3) Procedimiento :
[tex]-2x^2+1=-6\\\\-2x^2+1-1=-6-1\\\\-2x^2=-7\\\\\frac{-2x^2}{-2}=\frac{-7}{-2}\\\\x^2=\frac{7}{2}\\\\x=\sqrt{\frac{7}{2}},\:x=-\sqrt{\frac{7}{2}}[/tex]
4) Procedimiento:
[tex]2\left(x-4\right)^2=-5\\\\\frac{2\left(x-4\right)^2}{2}=\frac{-5}{2}\\\\\left(x-4\right)^2=-\frac{5}{2}\\\\x-4=\sqrt{-\frac{5}{2}}\\\\x-4=\sqrt{-1}\sqrt{\frac{5}{2}}\\\\x-4+4=i\sqrt{\frac{5}{2}}+4\\\\x=i\sqrt{\frac{5}{2}}+4\\\\x-4=-\sqrt{-\frac{5}{2}}\\\\\sqrt{-\frac{5}{2}}\\\\=\sqrt{-1}\sqrt{\frac{5}{2}}\\\\=i\sqrt{\frac{5}{2}}\\\\x-4=-i\sqrt{\frac{5}{2}}\\\\x-4+4=-i\sqrt{\frac{5}{2}}+4\\\\x=-i\sqrt{\frac{5}{2}}+4\\\\x=i\sqrt{\frac{5}{2}}+4,\:x=-i\sqrt{\frac{5}{2}}+4[/tex]
