Factorizaciones

1. x2 - 16=0 x2 = 16 x = -4

o x =4 x=±42.

x2 + 3x – 10 = 0 x2 + 3x =10 x2 + 3x + 9/4 = 49/4 (x+3/2)2 = 49/4 x + 3/2 = 7/2 x + 3/2 = -7/2

x+3/2=7/2 x=-5

x+3/2=7/2 x + -5

x=23.

x2 – 8x + 15 = 0 x2 - 8x = -15 x2 - 8x + 16 = 1 (x-4)2= 1 x-4 = 1 x-4=-1

x-4=1 x=3

x-4=1 x=3

x=54.

x2 – 5x = 0 x2 - 5x + 25/4 = 25/4 (9x – 5/3)2 = 25/4 x- 5/2 = 5/2 x - 5/2 = -5/2

x-5/2 = 5/2 x=0

x-5/2 = 5/2 x=0

o x=55.

x2 – 4x + 4=0 (x-2)2 = 0 x – 2 =0 x=26.

x2 – 2x – 24 =0 x2 – 2x = 24 x2 -2x + 1 = 25 (x-1)2 = 25 x – 1 = 5 x – 1 =-5

x-1=5 x=-4

x-1=5 x=-4

x=67.

2x2 – 11x – 6 = 0 x2 – 11x /2-3

= 0 x2 – 11 x/2 = 3 x2 - 11x/2 + 121/ 16 = 169/16 (x-11/4)2 = 169/16 x-11/4=13/4 x-11/4=-13/4

x-11/4=13/4 x=-1/2

-11/4=13/4 x=-1/2

x=68.

3x2 + 2x – 1 = 0 x2 + 2x/3 = 1/3 x2 + 2x/3 = 1/3 x2 + 2x/3 + 1/9 = 4/9 (x+1/3)2 = 4/9 x+1/ 3 2/3 x+1/3 =-2/3

x+1/3=2/3 x=-1

x+1/3= 1/3 x=-1

x=1/39.

3x2 – 7x – 6 = 0 x2 - 7x/3 =2 x2-7x/3 + 49 /36 = 121/36 (x-7/6)2=121/36 x- 7/6 = 11/6 x-7/6=-11/6

x-7/6=11/6 x=-2/3

x-7/6=11/6 x=-2/3

x=310.

6x2 – 11 x + 3 = 0 x2-11x/6 + 1/2 = 0 x2-11x/6=-1/2 x2- 22x/6 + 121/144=49/144 (x-11/12)2 = 49/144 x-11/12 = 7/12 x-11/12=-7/12

x-11/12=7/12 x=1/3

x-11/12=7/12 x=1/3

x=3/2

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