5. Solution:

( 1)x？ +x- 12 = 0∶a = 1b = 1c =- 12 ∴b？ -4ac=49>0

∴ x = (-1√ 49)/2 = (-17)/2 The root of the original equation is x 1=-4 x2=3.

(2)x？ -√2x- 1/4 = 0∶a = 1 b =-√2c =- 1/4 ∴b？ -4ac=3>0

∴ x = (√ 2 √ 3)/2 The root of the original equation is x1= (√ 2+√ 3)/2x2 = (√ 2-√ 3)/2.

(3)x？ +4x+8=2x+ 1 1 The original equation is transformed into x? +2x-3 = 0∶a = 1b = 2c =-3

∴b？ -4ac =16 > 0 ∴ x = (-2 √16)/2×1=-1∴ The root of the original equation is

x 1=-3 x2= 1

(4)x(x-4)=2-8x The original equation is transformed into x? +4x-2 = 0∶a = 1b = 4c =-2

∴b？ -4ac = 24 > 0 ∴x=(-4√24)/2× 1 =-2√6

The root of the original equation is x 1=-2+√6 x2=-2-√6.

(5)x？ +2x = 0∫a = 1b = 2c = 0 ∴b？ -4ac=4>0

∴ x = (-2 √ 4)/2×1=-1∴ The root of the original equation is x 1=0 x2=-2.

(6)x？ +2√5x+ 10 = 0∶a = 1b = 2√5c = 10 ∴b？ -4ac=-20