F4-解一元二次方程

5分咁多題...
1)x^2+x-42=0
(x+7)(x-6)=0
x=-7 or x= 6 #

2) 4x^2-9=0
(2x-3)(2x+3)=0
x= 3/2 or x= -3/2 #

3) 2x^2-32=0 ??
x^2-16=0
(x-4)(x+4)=0
x= 4 or x= -4 #

4)25+4(5x-x^2)=0
25+20x-4x^2=0
-4x^2+20x+25=0
4x^2-20x-25=0
x= -(-20)±√[(-20)^2-4(4)(-25)] / 2(4)
= 20±√800 / 8
=20±20√2 / 8
=5±5√2 / 2
i.e. x=(5+5√2) / 2 or x=(5-5√2) / 2 #

5) (2+x)(9x-7)=2+x
(2+x)(9x-7-1)=0
(2+x)(9x-8)=0
x= -2 or x= 8/9 #

6) (6x-5)(1+x)=1+2x+x^2
(6x-5)(1+x)=(1+x)^2
(1+x)^2 - (6x-5)(1+x)=0
(1+x)[(1+x)-(6x-5)]=0
(1+x)(6-5x)=0
x= -1 or x= 6/5 #

7) (x-4)(x-5) = -1/4
x^2-9x+20 = -1/4
4x^2-36x+81=0
(2x-9)^2=0
x=9/2 (repeated) //

8) 6=(x+7)^2
x+7=±√6
x=±√6 - 7
i.e. x=√6 -7 or x=-√6 - 7 #

1)
x^2+x-42=0
x=6 或 x=7

2)
4x^2-9=0
x^2=9/4
x=3/2或 x=-3/2

3)
2x^2-32=0
x=4或 x=-4

4)
25+4(5x-x^2)=0
-4x^2+20x+25=0
x=-1.04 或 x=6.04

5)
(2+x)(x-7)=2+x
x^2-7x+2x-14=2+x
x^2-6x-16=0
x=8或 x=-2

6)
(6x-5)(1+x)=1+2x+x^2
6x+6x^2-5-5x=1+2x+x^2
5x^2-x-6=0
x=1.2或 x=-1

7)
(x-4)(x-5)=-1/4
x^2-5x-4x+20=-1/4
x^2-9x+79/4=0
x=5.21或 x=3.79

8)
6=(x+7)^2
6=x^2+14x+49
x^2+14x-43=0
x=2.59 或 x=-16.6

1)x^2+x-42=0
(x+7)(x-6)=0
x=-7 or x=6
2) 4x^2-9=0
(2x)^2-3^2=0
(2x-3)(2x+3)=0
2x-3=0 or 2x+3=0
2x=3 or 2x=-3
x=3/2 or x=-3/2
3) 2x^2-32=0
2(x^2-16)=0
x^2-4^2=0
(x-4)(x+4)=0
x=4 or x=-4
4)25+4(5x-x^2)????????????????????????????
=25+20x-4x^2
=-((2x)^2-20x-25)
=自己計埋落去
5)(2+x)9x-7)=2+x????????????????????????????????
(2+x)9x-7)=2+x
18x+9x^2-14-7x=2+x
9x^2+10x-16=0
x=(-10+-√(10^2-4(9)(-16)))/(2*9)
=自己計埋落去
6)(6x-5)(1+x)=1+2x+x^2
6x-5+6x^2-5x=x^2+2x+1
5x^2-x-6=0
x=(-1+-√((-1)^2-4(5)(-6)))/(2*5)
=自己計埋落去
7)(x-4)(x-5)=-1/4
x^2-4x-5x+20=-1/4
x^2-9x+5=0
x=(9+-√((-9)^2-4(5)))/2
=自己計埋落去
8)6=(x+7)^2
x+7=+-√6
x=+-√(6)-7