Math Grade 9, Volume I, Page 34 Exercise 1.2 (descending order-solving quadratic equation of one variable), both of which need detailed processes! ! ! ~

1. Fill in the blanks:

( 1)x^2+ 10x+25=(x+5)^2； (2)x^2- 12x+36=(x-6 )^2；

(3)x^2+5x+25/4 =(x+5/2)^2； ⑷x^2-(2/3)x+ 1/9=(x- 1/3 )^2.

2. Solve the following equation:

( 1)x^2+ 10x+9=0； (2)x^2-x-(7/4)=0；

(3)3x^2+6x-4=0； (4)4x^2-6x-3=0；

(5)x^2+4x-9=2x- 1 1； (6) x(x+4)=8x+ 12

The factorization of (1) gives (x+ 1)(x+9)=0, so X 1=- 1, x2 =-9x2-x-7/4 = 0.

(2) Multiply by 4 to get 4x 2-4x-7 = 0.

x =(-(-4)√(〖(-4)〗^2-4*4*(-7)))/(2*4)=(4 8√2)/8 =( 1 2√2)/2

(3)3x^2+6x-4=0

x^2+2x-4/3=0

x^2+2x+ 1- 1-4/3=0

(x+ 1)^2-7/3=0

(x+ 1)^2-2 1/9=0

(x+ 1-√2 1/3)(x+ 1+√2 1/3)= 0

X=√2 1/3- 1 or x=-√2 1/3- 1

(4)4x？ -6x-3=0

x？ -(3/2)x-3/4=0

(x-3/4)？ -(9/ 16)-(3/4)=0

(x-3/4)？ =2 1/ 16

So x = (3 √ 2 1)/4x? +4x-9=2x- 1 1

x？ +2x+2=0

(x+ 1)？ =- 1

No solution in real number range

(6)x(x+4)=8x+ 12

x？ +4x=8x+ 12

x？ +4x-8x- 12=0

x？ -4x- 12=0

(x-6)(x+2)=0

X=6 or x=-2.