1、經(jīng)典解法20題1）(3x+1)2=72）9x2-24x+16=11(3)(x+3)(x-6)=-8(4)2x2+3x=0(5)6x2+5x-50=0(選學）(6)x2-4x+4=0（選學）(7)（x-2）2=4（2x+3）28）y2+22y-4=09）（x+1）2-3（x+1)+2=010）x2+2ax-3a2=0（a為常數(shù)）(11)2x27x4(12)x212x13）x2+6x+5=0(14)x24x+3=0(15)7x24x3=0(16)x26x+9=0(17)x2+8x+16=9(18)(x2-5)2=16(19)x(x+2)=x(3-x)+1(20)6x2+x-2=0海量111題1)x

2、2-9x+8=0(2)x2+6x-27=0(3)x2-2x-80=0(4)x2+10 x-200=0(5)x2-20 x+96=0(6)x2+23x+76=0(7)x2-25x+154=0(8)x2-12x-108=0(9)x2+4x-252=0(10)x2-11x-102=0(11)x2+15x-54=0(12)x2+11x+18=0(13)x2-9x+20=0(14)x2+19x+90=0(15)x2-25x+156=0(16)x2-22x+57=0(17)x2-5x-176=0(18)x2-26x+133=0(19)x2+10 x-11=0(20)x2-3x-304=0(21)x2+13

3、x-140=0(22)x2+13x-48=0(23)x2+5x-176=0(24)x2+28x+171=0(25)x2+14x+45=0(26)x2-9x-136=0(27)x2-15x-76=0(28)x2+23x+126=0(29)x2+9x-70=0(30)x2-1x-56=0(31)x2+7x-60=0(32)x2+10 x-39=0(33)x2+19x+34=0(34)x2-6x-160=0(35)x2-6x-55=0(36)x2-7x-144=0(37)x2+20 x+51=0(38)x2-9x+14=0(39)x2-29x+208=0(40)x2+19x-20=0(41)x2-1

4、3x-48=0(42)x2+10 x+24=0(43)x2+28x+180=0(44)x2-8x-209=0(45)x2+23x+90=0(46)x2+7x+6=0(47)x2+16x+28=0(48)x2+5x-50=0(49)x2+13x-14=0(50)x2-23x+102=0(51)x2+5x-176=0(52)x2-8x-20=0(53)x2-16x+39=0(54)x2+32x+240=0(55)x2+34x+288=0(56)x2+22x+105=0(57)x2+19x-20=0(58)x2-7x+6=0(59)x2+4x-221=0(60)x2+6x-91=0(61)x2+8x

5、+12=0(62)x2+7x-120=0(63)x2-18x+17=0(64)x2+7x-170=0(65)x2+6x+8=0(66)x2+13x+12=0(67)x2+24x+119=0(68)x2+11x-42=0(69)x20 x-289=0(70)x2+13x+30=0(71)x2-24x+140=0(72)x2+4x-60=0(73)x2+27x+170=0(74)x2+27x+152=0(75)x2-2x-99=0(76)x2+12x+11=0(77)x2+17x+70=0(78)x2+20 x+19=0(79)x2-2x-168=0(80)x2-13x+30=0(81)x2-10

6、 x-119=0(82)x2+16x-17=0(83)x2-1x-20=0(84)x2-2x-288=0(85)x2-20 x+64=0(86)x2+22x+105=0(87)x2+13x+12=0(88)x2-4x-285=0(89)x2+26x+133=0(90)x2-17x+16=0(91)x2+3x-4=0(92)x2-14x+48=0(93)x2-12x-133=0(94)x2+5x+4=0(95)x2+6x-91=0(96)x2+3x-4=0(97)x2-13x+12=0(98)x2+7x-44=0(99)x2-6x-7=0(100)x2-9x-90=0(101)x2+17x+72

7、=0(102)x2+13x-14=0(103)x2+9x-36=0(104)x2-9x-90=0(105)x2+14x+13=0(106)x2-16x+63=0(107)x2-15x+44=0(108)x2+2x-168=0(109)x2-6x-216=0(110)x2-6x-55=0(111)x2+18x+32=0答案1）(3x+1)2=7解：(3x+1)2=7(3x+1)2=73x+1=7(注意不要丟解)x=(7-1)/32）9x2-24x+16=11解：9x2-24x+16=11(3x-4)2=113x-4=11x=(11+4)/3原方程的解為x1=(11+4)/3x2=(-11+4)/

8、3(3)(x+3)(x-6)=-8解：(x+3)(x-6)=-8化簡整理得x2-3x-10=0(方程左側(cè)為二次三項式，右側(cè)為零)(x-5)(x+2)=0(方程左側(cè)分解因式)x-5=0或x+2=0(轉(zhuǎn)變成兩個一元一次方程)x1=5,x2=-2是原方程的解。(4)2x2+3x=0解：2x2+3x=0 x(2x+3)=0(用提公因式法將方程左側(cè)分解因式)x=0或2x+3=0(轉(zhuǎn)變成兩個一元一次方程)x1=0，x2=-3/2是原方程的解。注意：有些同學做這類題目時簡單扔掉x=0這個解，應記著一元二次方程有兩個解。(5)6x2+5x-50=0(選學）解：6x2+5x-50=0(2x-5)(3x+10)=

9、0(十字相乘分解因式時要特別注意符號不要犯錯)2x-5=0或3x+10=0 x1=5/2,x2=-10/3是原方程的解。(6)x2-4x+4=0（選學）解：x2-4x+4=0(x-2)(x-2)=0（4可分解為22，本題可用因式分解法）x1=2,x2=2是原方程的解。(7)（x-2）2=4（2x+3）2解.(x-2)2-4(2x+3)2=0.x-2+2(2x+3)(x-2-2(2x+3)=0.(5x+4)(-5x-8)=0.x1=-4/5,x2=-8/58）y2+22y-4=0解(y+2)2-2-4=0.(y+2)2=6.y+2=6.y=-26.y1=-2+6；y2=-2-6.9）（x+1）2

10、-3（x+1)+2=0解(x+1-1)(x+1-2)=0.x(x-1)=0.x1=0,x2=1.10）x2+2ax-3a2=0（a為常數(shù)）解(x+3a)(x-a)=0.x1=-3a,x2=a.(11)2x27x4解：方程可變形為2x27x40a2，b7，c4，b24ac7242(4)810，xx1，x24(12)x212x解：方程可變形為x22x10a1，b2，c1，b24ac(2)241(1)160 xx12，x2213）x2+6x+5=0解：原方程可化為(x+5)(x+1)=0 x1=-5x2=-1(14)x24x+3=0解：原方程可化為(x-3)(x-1)=0 x1=3x2=1(15)7

11、x24x3=0解原方程可化為(7x+3)(x-1)=0 x1=-3/7x2=1(16)x26x+9=0解原方程可化為(x-3)2=0 x1=x2=3(17)x2+8x+16=9解：(x+4)2=9x+4=3或x+4=-3x1=-1,x2=-7(18)(x2-5)2=16解：x2-5=4或x2-5=-4x2=9或x2=1x1=3,x2=-3,x3=1,x4=-1(19)x(x+2)=x(3-x)+1解x2+2x=3x-x2+12x2-x-1=0(2x+1)(x-1)=0 x1=-1/2x=1(20)6x2+x-2=0解原方程可化為(3x+2)(2x-1)=0(x+2/3)(x-1/2)=0 x1

12、=-2/3x2=1/2這是20道有過程的，還有一些沒有過程，只有答案的。1)x2-9x+8=0答案：x1=8x2=1(2)x2+6x-27=0答案：x1=3x2=-9(3)x2-2x-80=0答案：x1=-8x2=10(4)x2+10 x-200=0答案：x1=-20 x2=10(5)x2-20 x+96=0答案：x1=12x2=8(6)x2+23x+76=0答案：x1=-19x2=-4(7)x2-25x+154=0答案：x1=14x2=11(8)x2-12x-108=0答案：x1=-6x2=18(9)x2+4x-252=0答案：x1=14x2=-18(10)x2-11x-102=0答案：x1

13、=17x2=-6(11)x2+15x-54=0答案：x1=-18x2=3(12)x2+11x+18=0答案：x1=-2x2=-9(13)x2-9x+20=0答案：x1=4x2=5(14)x2+19x+90=0答案：x1=-10 x2=-9(15)x2-25x+156=0答案：x1=13x2=12(16)x2-22x+57=0答案：x1=3x2=19(17)x2-5x-176=0答案：x1=16x2=-11(18)x2-26x+133=0答案：x1=7x2=19(19)x2+10 x-11=0答案：x1=-11x2=1(20)x2-3x-304=0答案：x1=-16x2=19(21)x2+13x

14、-140=0答案：x1=7x2=-20(22)x2+13x-48=0答案：x1=3x2=-16(23)x2+5x-176=0答案：x1=-16x2=11(24)x2+28x+171=0答案：x1=-9x2=-19(25)x2+14x+45=0答案：x1=-9x2=-5(26)x2-9x-136=0答案：x1=-8x2=17(27)x2-15x-76=0答案：x1=19x2=-4(28)x2+23x+126=0答案：x1=-9x2=-14(29)x2+9x-70=0答案：x1=-14x2=5(30)x2-1x-56=0答案：x1=8x2=-7(31)x2+7x-60=0答案：x1=5x2=-12

15、(32)x2+10 x-39=0答案：x1=-13x2=3(33)x2+19x+34=0答案：x1=-17x2=-2(34)x2-6x-160=0答案：x1=16x2=-10(35)x2-6x-55=0答案：x1=11x2=-5(36)x2-7x-144=0答案：x1=-9x2=16(37)x2+20 x+51=0答案：x1=-3x2=-17(38)x2-9x+14=0答案：x1=2x2=7(39)x2-29x+208=0答案：x1=16x2=13(40)x2+19x-20=0答案：x1=-20 x2=1(41)x2-13x-48=0答案：x1=16x2=-3(42)x2+10 x+24=0答

16、案：x1=-6x2=-4(43)x2+28x+180=0答案：x1=-10 x2=-18(44)x2-8x-209=0答案：x1=-11x2=19(45)x2+23x+90=0答案：x1=-18x2=-5(46)x2+7x+6=0答案：x1=-6x2=-1(47)x2+16x+28=0答案：x1=-14x2=-2(48)x2+5x-50=0答案：x1=-10 x2=5(49)x2+13x-14=0答案：x1=1x2=-14(50)x2-23x+102=0答案：x1=17x2=6(51)x2+5x-176=0答案：x1=-16x2=11(52)x2-8x-20=0答案：x1=-2x2=10(53

17、)x2-16x+39=0答案：x1=3x2=13(54)x2+32x+240=0答案：x1=-20 x2=-12(55)x2+34x+288=0答案：x1=-18x2=-16(56)x2+22x+105=0答案：x1=-7x2=-15(57)x2+19x-20=0答案：x1=-20 x2=1(58)x2-7x+6=0答案：x1=6x2=1(59)x2+4x-221=0答案：x1=13x2=-17(60)x2+6x-91=0答案：x1=-13x2=7(61)x2+8x+12=0答案：x1=-2x2=-6(62)x2+7x-120=0答案：x1=-15x2=8(63)x2-18x+17=0答案：x

18、1=17x2=1(64)x2+7x-170=0答案：x1=-17x2=10(65)x2+6x+8=0答案：x1=-4x2=-2(66)x2+13x+12=0答案：x1=-1x2=-12(67)x2+24x+119=0答案：x1=-7x2=-17(68)x2+11x-42=0答案：x1=3x2=-14(69)x20 x-289=0答案：x1=17x2=-17(70)x2+13x+30=0答案：x1=-3x2=-10(71)x2-24x+140=0答案：x1=14x2=10(72)x2+4x-60=0答案：x1=-10 x2=6(73)x2+27x+170=0答案：x1=-10 x2=-17(74

19、)x2+27x+152=0答案：x1=-19x2=-8(75)x2-2x-99=0答案：x1=11x2=-9(76)x2+12x+11=0答案：x1=-11x2=-1(77)x2+17x+70=0答案：x1=-10 x2=-7(78)x2+20 x+19=0答案：x1=-19x2=-1(79)x2-2x-168=0答案：x1=-12x2=14(80)x2-13x+30=0答案：x1=3x2=10(81)x2-10 x-119=0答案：x1=17x2=-7(82)x2+16x-17=0答案：x1=1x2=-17(83)x2-1x-20=0答案：x1=5x2=-4(84)x2-2x-288=0答案：x1=18x2=-16(85)x2-20 x+64=0答案：x1=16x2=4(86)x2+22x+105=0答案：x1=-7x2=-15(87)x2+13x+12=0答案：x1=-1x2=-12(88)x2-4x-285=0答案：x1=1