超急, Factorizing equations

1)a) 2x^2 + 11x + 5
=(2x + 1)(x + 5) //

b) 3p^2 + 2x + 3
=(3p - 3)(p - 1)
=3(p - 1)(p - 1)
=3(p - 1)^2 //

2)a) x^2 + 2x - 13 = 0
x^2 + 2x + 1 - 1 - 13 = 0
x^2 + 2x + 1 - 14 = 0
(x + 1)^2 - 14 = 0
x + 1 = 14^(1/2)
x + 1 = 3.741 or -3.741
x = 2.741 or -4.741 //

b) x^2 - 5x - 3 = 0
x^2 - 2(2.5)x + (2.5)^2 - (2.5)^2 - 3 = 0
(x - 2.5)^2 - 9.25 = 0
(x - 2.5) = 3.041 or -3.041
x = 5.541 or -0.541 //

1a (2x+1)(x+5)
b 3(p-1)^2

2a x = +/- 14^0.5 - 1
b x = +/- 9.25^0.5 + 2.5

1) a) 2x^2 + 11x + 5 = (2x + 1)(x + 5)

b) 3p^2 - 6p + 3 = 3(p^2 - 2p + 1) = 3(p-1)^2

2a) x^2 + 2x - 13 = 0
=> x^2 + 2x + 1 - 13 = 1
=> (x+1)^2 - 13 = 1
=> (x+1)^2 = 14
=> x+1 = 14^(1/2) or -14^(1/2)
=> x = 14^(1/2) - 1 or -14^(1/2) - 1
=> x = 2.742 or -4.742

b) 2x^2 - 10x - 6 = 0
=> x^2 - 5x - 3 = 0
=> x^2 - 5x + (5/2)^2 - 3 = (5/2)^2
=> (x - 5/2)^2 - 3 = (5/2)^2
=> (x - 5/2)^2 = (5/2)^2 - 3
=> x - 5/2 = (13/4)^(1/2) or -(13/4)^(1/2)
=> x = (13/4)^(1/2) + 5/2 or -(13/4)^(1/2) + 5/2
=> x = 4.303 or 0.697

2007-11-06 10:19:41 補充：
2b) 2x^2 - 10x - 6 = 0=> x^2 - 5x - 3 = 0=> x^2 - 5x + (5/2)^2 - 3 = (5/2)^2=> (x - 5/2)^2 - 3 = (5/2)^2=> (x - 5/2)^2 = (5/2)^2 + 3=> x - 5/2 = (37/4)^(1/2) or -(37/4)^(1/2)=> x = (37/4)^(1/2) + 5/2 or -(37/4)^(1/2) + 5/2=> x = 5.541 or -0.542

1
a) (2x+1)(x+5)
b) 3(p-1)^2

2
a) x = +/- 14^0.5 - 1
b) x = +/- 9.25^0.5 + 2.5