1, (1)169x-1= 0 (transfer term, direct Kaiping method)

X^2= 1/ 169

X= 1/ 13，

Write x1=113, x2 =-113 (the same below).

⑵ 4x 2+ 12x+9 = 8 1 (formula, direct Kaiping method)

(2X+3)^2=8 1

2X+3= 9

X 1=3，X2=-6

(3) x 2-7x- 1 = 0 (formula method)

Δ=49+4=53

X=(7 √53)/2

(4) 2x 2+3x = 3 (shift term, formula method)

2X^2+3X-3=0

Δ=9+24=33

X=(-3 √33)/4

5] x 2-2x+ 1 = 25 (formula, direct root)

(X- 1)^2=25

X- 1= 5

X= 1 5

X 1=6，X2=-4

[6] x (2x-5) = 4x- 10 (arranged in general form)

2x 2-9x+ 10 = 0 (factorization)

(2X-5)(X-2)=0

X 1=5/2，X2=2 .

(7) x 2+5x+7 = 3x+ 1 1 (arranged in general form)

X^2+2X=4

(X+ 1)^2=5

X= 1 √5

Being1-8x+16x2 = 2-8x (observation features, decomposition factors)

( 1-4X)^2=2( 1-4X)

( 1-4X)[( 1-4X)-2]=0

1-4X=0 or -4X- 1=0.

X 1= 1/4，X2=- 1/4。 (Of course, it can also be changed into a general form and directly leveled).

Levies x2-5x-10 = 0 (formula method)

Δ=25+40=65

X=(5 √65)/2

⑽ 2x 2+7x+ 1 = 0 (formula method)

Δ=49-8=4 1

X=(-7 √4 1)/4

⑾3X^2- 1=2X+5

3X^2-2X-6=0

Δ=4+72=76=4× 19

x =(2 ^ 2√ 19)/6 =( 1√ 19)/3

⑿X(X- 1)=3X+7

X^2-4X-7=0

Δ= 16+28=42

X=(4 √42)/2

2. Let one number be x and the other number be (8-X).

X(8-X)=9.75，

X^2-8X+9.75=0

(X-4)^2=6.25

X=4 2.5

X 1=6.5，X2=- 1.5，

∴ These two numbers are 6.5, 1.5 or-1.5 and -6.5 respectively.

3. Let the short side of the rectangle be x and the long side be (X+3). According to the meaning of the question:

X(X+3)=4, x 2+3x-4 = 0, (X- 1)(X+4)+0, X= 1 (take positive).

On the other side: X+3=4,

Diagonal length: √ (1 2+3 2) = √ 10.

4. What's the topic?