Question

resolva as equaçoes do 2° grau imcompletas e indique o con junto soluçao
1) - 8x² - 32x = 0 2) 9t - 18t²= 0 3)15x²= - 25x 4) - 6x² +54 = 0 5) 3x² - 36 = 0

6)18x² = 2

Answer 1

$1) - 8 x^{2} - 32x = 0\to\\\\ x(-8x-32)=0\\\\ x=0 \\\\ -8x-32=0\to -8x=32\to x= \frac{32}{-8} \to x=-4\\\\\\ S= \left \{ -4;0\left \}$





$2) 9t - 18t^2= 0\\\\ t(-18t+9)=0\\\\ t=0\\\\ -18t+9=0\to -18t=-9\to t= \frac{-9}{-18} \to t= \frac{1}{2} \\\\\\ S= \left \{0; \frac{1}{2}\left \}$





$3)15 x^{2} = - 25x \to 15 x^{2} +25x =0\\\\ x(15x+25)=0\\\\ x=0\\\\ 15x+25=0\to 15x=-25\to x= \frac{-25}{15} \to x=- \frac{5}{3} \\\\\\ S= \left \{ - \frac{5}{3};0\left \}$





$4) - 6 x^{2} +54 = 0\to\\\\ - 6 x^{2} =-54\to \\\\ x^{2} = \frac{-54}{-6} \to \\\\ x^{2} =9\to \\\\ x=\pm \sqrt{9} \to \\\\x=\pm 3\\\\\\ S= \left \{ -3;3\left \}$





$5) 3 x^{2} - 36 = 0\to\\\\ 3 x^{2}= 36 \to \\\\ x^{2} = \frac{36}{3} \to\\\\ x^{2} =12\to\\\\ x=\pm \sqrt{12} \to \\\\ x=\pm \sqrt{2^2*3} \to \\\\ x=\pm 2\sqrt{3} \\\\\\ S= \left \{-\pm 2\sqrt{3};\pm 2\sqrt{3}\left \}$





$6)18 x^{2} = 2\to \\\\ x^{2} = \frac{2}{18} \to \\\\ x^{2} = \frac{1}{9} \to \\\\x=\pm \sqrt{ \frac{1}{9} } \to \\\\x=\pm \frac{1}{3} \\\\\\ S= \left \{-\frac{1}{3};\frac{1}{3}\left \}$


Prontinho... :)