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解:?$x^2-6x = 7$?
?$ x^2-6x + 9 = 7 + 9$?
?$ (x - 3)^2=16$?
?$ x - 3=\pm 4$?
?$ x_{1}=7,$??$x_{2}=-1$?
解:?$x^2+10x + 9 = 0$?
?$ x^2+10x + 25=-9 + 25$?
?$ (x + 5)^2=16$?
?$ x + 5=\pm 4$?
?$x_{1}=-1,$??$x_{2}=-9$?
解:?$x^2+2x = 7$?
?$ (x + 1)^2=8$?
?$ x + 1=\pm 2\sqrt {2}$?
?$ x_{1}=-1 + 2\sqrt {2},$??$x_{2}=-1 - 2\sqrt {2}$?
解:?$x^2-6x - 1 = 0$?
?$x^2-6x + 9 = 1 + 9$?
?$ (x - 3)^2=10$?
?$ x - 3=\pm \sqrt {10}$?
?$ x_{1}=3+\sqrt {10},$??$x_{2}=3-\sqrt {10}$?
解:?$t^2-t = 2$?
?$ t^2-t+\frac {1}{4}=2+\frac {1}{4}$?
?$ (t-\frac {1}{2})^2=\frac {9}{4}$?
?$ t-\frac {1}{2}=\pm \frac {3}{2}$?
?$ t_{1}=2,$??$t_{2}=-1$?
解:?$x^2-3=-3x$?
?$ x^2+3x+\frac {9}{4}=3+\frac {9}{4}$?
?$ (x+\frac {3}{2})^2=\frac {21}{4}$?
?$ x+\frac {3}{2}=\pm \frac {\sqrt {21}}{2}$?
?$ x_{1}=\frac {-3 + \sqrt {21}}{2},$??$x_{2}=\frac {-3 - \sqrt {21}}{2}$?
解:?$2x^2-5x = 0$?
?$x^2-\frac {5}{2}x=0$?
?$x^2-\frac {5}{2}x+\frac {25}{16}=\frac {25}{16}$?
?$(x-\frac {5}{4})^2=\frac {25}{16}$?
?$x-\frac {5}{4}=±\frac {5}{4}$?
?$x_{1}=0,$??$x_{2}=\frac {5}{2}$?
解:?$2x^2+3x + 1 = 0$?
?$x^2+\frac {3}{2}x=-\frac {1}{2}$?
?$x^2+\frac {3}{2}x+\frac {9}{16}=-\frac {1}{2}+\frac {9}{16}$?
?$(x+\frac {3}{4})^2=\frac {1}{16}$?
?$x+\frac {3}{4}=±\frac {1}{4}$?
?$x_{1}=-\frac {1}{2},$??$x_{2}=-1$?
解:?$3x^2-x - 2 = 0$?
?$x^2-\frac {1}{3}x=\frac {2}{3}$?
?$x^2-\frac {1}{3}x+\frac {1}{36}=\frac {2}{3}+\frac {1}{36}$?
?$(x-\frac {1}{6})^2=\frac {25}{36}$?
?$x-\frac {1}{6}=±\frac {5}{6}$?
?$x_{1}=-\frac {2}{3},$??$x_{2}=1$?
解:?$4x^2-2x - 1 = 0$?
?$x^2-\frac {1}{2}x=\frac {1}{4}$?
?$x^2-\frac {1}{2}x+\frac {1}{16}=\frac {1}{4}+\frac {1}{16}$?
?$(x-\frac {1}{4})^2=\frac {5}{16}$?
?$x-\frac {1}{4}=±\frac {\sqrt 5}4$?
?$x_{1}=\frac {1 + \sqrt {5}}{4},$??$x_{2}=\frac {1 - \sqrt {5}}{4}$?