二次公式(20點)...........

1.(3x+2)(3x-2)+3x=0
(3x)^2-(2)^2+3x=0
9x^2+3x-4=0
Method 1
By machine, x=0.52 or x=-0.85
Method 2
x= {-3 ± √ [(3)^2-4(9)(-4)] } / 2(9)
x=0.52 or x=-0.85

2.x(3x+4)=(x+1)(x-2)
3x^2+4x=x^2-x-2
2x^2+5x+2=0
Method 1
By machine, x=-0.5 or x=-2
Method 2
x= {-5 ± √ [(5)^2-4(2)(2)] } / 2(2)
x=-0.5 or x=-2

3.(x+0.5)(x+1)=-(3x/4)
x^2+1.5x+0.5=3x/4
4x^2+6x+2=-3x
4x^2+9x+2=0
Method 1
By machine, x=-0.25 or x=-2
Method 2
x= {-9 ± √ [(9)^2-4(4)(2)] } / 2(4)
x=-0.25 or x=-2

4.(x-3)(2x-5)=x(x+3)+2
2x^2-5x-6x+15=x^2+3x+2
x^2-14x+13=0
Method 1
By machine, x=1 or x=13
Method 2
x= {14 ± √ [(-14)^2-4(1)(13)] } / 2(1)
x=1 or x=13

5.(2x-3)^2+6x=7
(2x-3)(2x-3)+6x-7=0
4x^2-2(2x)(3)+6x-7=0
4x^2-12x+9+6x-7=0
4x^2-6x+2=0
Method 1
By machine, x=0.5 or x=1
Method 2
x= {6 ± √ [(-6)^2-4(4)(2)] } / 2(4)
x=0.5 or x=1

6.(x-3)^2=(2x+1)(x-2)
(x-3)(x-3)=2x^2-4x+x-2
x^2-6x+9=2x^2-3x-2
-x^2-3x+11=0
Method 1
By machine, x=-5.14 or x=2.14
Method 2
x= {3 ± √ [(-3)^2-4(-1)(11)] } / 2(-1)
x=-5.14 or x=2.14

1.(3x+2)(3x-2)+3x=0
(3x)^2-(2)^2+3x=0
9x^2+3x-4=0
Method 1
By machine, x=0.52 or x=-0.85
Method 2
x= {-3 ± √ [(3)^2-4(9)(-4)] } / 2(9)
x=0.52 or x=-0.85

2.x(3x+4)=(x+1)(x-2)
3x^2+4x=x^2-x-2
2x^2+5x+2=0
Method 1
By machine, x=-0.5 or x=-2
Method 2
x= {-5 ± √ [(5)^2-4(2)(2)] } / 2(2)
x=-0.5 or x=-2

3.(x+0.5)(x+1)=-(3x/4)
x^2+1.5x+0.5=3x/4
4x^2+6x+2=-3x
4x^2+9x+2=0
Method 1
By machine, x=-0.25 or x=-2
Method 2
x= {-9 ± √ [(9)^2-4(4)(2)] } / 2(4)
x=-0.25 or x=-2

4.(x-3)(2x-5)=x(x+3)+2
2x^2-5x-6x+15=x^2+3x+2
x^2-14x+13=0
Method 1
By machine, x=1 or x=13
Method 2
x= {14 ± √ [(-14)^2-4(1)(13)] } / 2(1)
x=1 or x=13

5.(2x-3)^2+6x=7
(2x-3)(2x-3)+6x-7=0
4x^2-2(2x)(3)+6x-7=0
4x^2-12x+9+6x-7=0
4x^2-6x+2=0
Method 1
By machine, x=0.5 or x=1
Method 2
x= {6 ± √ [(-6)^2-4(4)(2)] } / 2(4)
x=0.5 or x=1

6.(x-3)^2=(2x+1)(x-2)
(x-3)(x-3)=2x^2-4x+x-2
x^2-6x+9=2x^2-3x-2
-x^2-3x+11=0
Method 1
By machine, x=-5.14 or x=2.14
Method 2
x= {3 ± √ [(-3)^2-4(-1)(11)] } / 2(-1)
x=-5.14 or x=2.14

2007-11-07 01:06:00 補充：
In Method 1在答題不需要加入By machine。