F.4 Maths 一題

2x^2+x-3=0
2(x^2+x/2)-3=0
2[x^2+x/2+(1/4)^2-(1/4)^2]-3=0
2(x+1/4)^2-1/8-3=0
2(x+1/4)^2-25/8=0
(x+1/4)^2=25/16
x+1/4=5/4 or x+1/4=-5/4
x=1 or x=-3/2

2010-09-12 12:02:22 補充：
3x^2+4x-5=0
3[x^2+(4/3)x]-5=0
3[x^2+(4/3)x+(2/3)^2-(2/3)^2]-5=0
3(x+2/3)^2-19/3=0
(x+2/3)^2=19/9
x+2/3=√19/3 or x+2/3=-√19/3
x=(√19-2)/3 or x=-(√19+2)/3

2x^2+x-3=0
(2X+3)(X-1)=0
so,x=1 or -1/2

3x^2+4x-5=0

(This equation cannot use the completing square, it can only use the formular)
its means

-b+- square root (b)^2-4ac / 2a

2010-09-16 18:40:21 補充：
第一題是-1.5
也就是-3/2

2x^2+x-3=0
=> (x-1)(2x+3)=0
=> x=1, -3/2