Quadratic equation

1.(x-5)2-9=0
(x-5)2=9
x-5=3 or x-5=-3
x=8 or x=2


2.(x+4)(2x-3)=5(x+4)
x+4=0 or 2x-3=5
x=-4 or x=4

3.2x2-6x+3=0
x2-3x+3/2=0
x2-3x+9/4=-3/2+9/4
(x-3/2)2=3/4
x-3/2=√3/2 or x-3/2=-√3/2
x=(3+√3)/2 or x=(3-√3)/2

4.4x2+2+5x=0
4x2+5x+2=0
x2+5/4x+1/2=0
x2+5/4x+25/64=-1/2+25/64
(x+5/8)2=-7/64
∵√(-7/64) is not a real number.
∴The equation has no real roots.

5.3x(x-3)+4=0
3x2-9x+4=0
x2-3x+4/3=0
x2-3x+9/4=-4/3+9/4
(x-3/2)2=11/12
x-3/2=√(11/12) or x-3/2=-√(11/12)
x=3/2+√(11/12) or x=3/2-√(11/12)

6.42-24+p=0
16-24+p=0
-8+p=0
p=8

2009-12-06 22:17:19 補充：
上面第4題做錯了。

4x^2+2=5x
4x^2-5x+2=0
x^2 -5/2x+1/2=0
x^2 -5/2x+25/16=-1/2+25/16
(x-5/4)^2=17/16
x-5/4=√17/4 or x-5/4=-√17/4
x=(5+√17)/4 or x=(5-√17)/4