(x+3)(x+7)=0

x 1=-3 x2=-7

x*-x- 1=0

x *-x- 1+ 1.25 = 0+ 1.25

(x-0.5)*= 1.25

x-0.5= √ 1.25

x 1 =√ 1.25+0.5 x2 =-√ 1.25+0.5

? 3x*+6x-4=0

△=b？ ﹣4ac=36+48=84

x=[-b √(b？ -4ac)]/2a=(-6 √84)/6

x 1 =(-6+√84)/6 x2 =(-6-√84)/6

3x(x+ 1)=3x+3

3x*+3x-3x-3=0

3x*-3=0

3(x*- 1)=0

x 1=- 1 x2= 1

4x*-4x+ 1=x*+6x+9

4x*-4x+ 1-x*-6x-9=0

3x*- 10x-8=0

(x-4)(3x+2)=0

x 1=4 x2=-3/2

7x*-√6x-5=0

△=b？ ﹣4ac=6+ 140= 146

x=[-b √(b？ -4ac)]/2a=(√6 √ 146)/2

? x 1=(√6-√ 146)/2

? x2=(√6+√ 146)/2

2. let the smaller one be x? The other is x+2.

x(x+2)= 168

x*+2x- 168=0

(x- 12)(x+ 14)=0

x 1= 12 x2=- 14

When x is 12, x+2= 14.

When x is-14, x+2=- 12.

The two even numbers are 12, 14 or-12 and-14 respectively.

3. Let one side be X and the other side be14-X.

? x( 14-x)÷2=24

14x-x* =48

x*- 14+48=0

? (x-6)(x-8)=0

x 1=6？ x2=8

When x is 6, 14-x=8.

When x is 8, 14-x=6.

∴ becomes 8,6 at two right angles.

4. For small branches, let each branch be x long.

? 1+x+x*=9 1

? x+x*=90

x*+x-90=0

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

? x 1=9？ X2=- 10 (not in conformity with the meaning of the question, omitted)

∴ Each branch is a twig with a length of 9.

5. Let one diagonal line be x cm and the other line be 10-x cm.

? x( 10-x)÷2= 12

10x-x*-24=0

x*- 10+24=0

△=b？ ﹣4ac= 100-96=4

? x=[-b √(b？ -4ac)]/2a=( 10 2)/2

x 1=4？ x2=6

Diagonal lines of diamonds are 4cm and 6cm respectively.

The side length of a diamond is √ (4/2) *+(6/2) * = √ 4+9 = √13 √ 3.6.

C diamond =4×3.6= 14.4.

6.？ * * * There are X teams participating in the competition.

? x(x- 1)=90

? x*-x-90=0

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

X 1= 10 x2=-9 (omitted).

* * * There are 10 teams participating.