（1）解，得：ax^2+bx+c=0兩邊同除以a得x^2+(b/a)x+c/a=0x^2+b/ax+(b/2a)^2=(b/2a)^2-c/a(x+b/2a)^2=(b^2-4ac)/4a^2當b^2-4ac=0時x+b/2a=±(√b^2-4ac/2a)x=(-b±√b^2-4ac)/2a(2)解，得：x^2+4x+2=0X^2+4x+2=0x²＋4x＋x=2﹙x＋2﹚²＝2x＋2=±√2x=－2±√2(3)解，得：（2x-1）^2=x(3x+2)-7（2 x - 1）² = x（3 x + 2）- 74 x ² - 4 x + 1 = 3 x ² + 2 x - 7x ² - 6 x + 8 = 0（x - 2）（x - 4）= 0x - 2 = 0 或 x - 4 = 0x₁ = 2 x₂ = 4(4)解，得：x^2-3x-2=0x^2-3x-2=0x^2-2*(3/2)x+(3/2)^2-(3/2)^2-2=0(x-3/2)^2=(3/2)^2+2(x-3/2)^2=9/4+2(x-3/2)^2=17/4x-3/2=±（√17）/2x=±（√17）/2+3/2x1=（√17）/2+3/2=（√17+3)/2x2=-（√17）/2+3/2=（-√17+3)/2（5）解，得：2x^2-5x+2=02x^2－5x＋2＝0x^2－5/2x＋1＝0x^2－5/2x＋(5/4)^2 -(5/4)^2 +1＝0(x-5/4)^2 =9/16x-5/4 =3/4或x-5/2 =-3/4x=2或x =1/2(6)x^2+根號3x-1=0（7）x^2-3x-1=0解，得：x²－3x=1x²－3x＋﹙3／2﹚²＝1＋﹙3／2﹚²﹙x－3／2﹚²＝13／4x－3／2=±√13／2x1=﹙3＋√13﹚／2x2=﹙3－√13﹚／2（8）(x-3)^2=4x(x-3)解，得：x²-6x+9+4x²-12x=05x²-18x+9=0用公式x={-b±√（b^2－4ac）}/2a b²得：x1=3，x2=3\5(9)x^2-10x+9=0解，得：(x-1)(x-9)=0x=1或x=9(10)2x^2+1=3x解，得：2x^2-3x+1=0（2x-1）（x-1）=02x-1=0或x-1=0x1=1/2x2=1
（1）解，得：ax^2+bx+c=0兩邊同除以a得x^2+(b/a)x+c/a=0x^2+b/ax+(b/2a)^2=(b/2a)^2-c/a(x+b/2a)^2=(b^2-4ac)/4a^2當b^2-4ac=0時x+b/2a=±(√b^2-4ac/2a)x=(-b±√b^2-4ac)/2a(2)解，得：x^2+4x+2=0X^2+4x+2=0x²＋4x＋x=2﹙x＋2﹚²＝2x＋2=±√2x=－2±√2(3)解，得：（2x-1）^2=x(3x+2)-7（2 x - 1）² = x（3 x + 2）- 74 x ² - 4 x + 1 = 3 x ² + 2 x - 7x ² - 6 x + 8 = 0（x - 2）（x - 4）= 0x - 2 = 0 或 x - 4 = 0x₁ = 2 x₂ = 4(4)解，得：x^2-3x-2=0x^2-3x-2=0x^2-2*(3/2)x+(3/2)^2-(3/2)^2-2=0(x-3/2)^2=(3/2)^2+2(x-3/2)^2=9/4+2(x-3/2)^2=17/4x-3/2=±（√17）/2x=±（√17）/2+3/2x1=（√17）/2+3/2=（√17+3)/2x2=-（√17）/2+3/2=（-√17+3)/2（5）解，得：2x^2-5x+2=02x^2－5x＋2＝0x^2－5/2x＋1＝0x^2－5/2x＋(5/4)^2 -(5/4)^2 +1＝0(x-5/4)^2 =9/16x-5/4 =3/4或x-5/2 =-3/4x=2或x =1/2(6)x^2+根號3x-1=0（7）x^2-3x-1=0解，得：x²－3x=1x²－3x＋﹙3／2﹚²＝1＋﹙3／2﹚²﹙x－3／2﹚²＝13／4x－3／2=±√13／2x1=﹙3＋√13﹚／2x2=﹙3－√13﹚／2（8）(x-3)^2=4x(x-3)解，得：x²-6x+9+4x²-12x=05x²-18x+9=0用公式x={-b±√（b^2－4ac）}/2a b²得：x1=3，x2=3\5(9)x^2-10x+9=0解，得：(x-1)(x-9)=0x=1或x=9(10)2x^2+1=3x解，得：2x^2-3x+1=0（2x-1）（x-1）=02x-1=0或x-1=0x1=1/2x2=1