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6.
(1). x²+x+0.5²=1+0.25, (x+0.5)²=1.25=5/4, x=±√5/2-1/2=(±√5-1)/2.
(2). 3x²+6x-1=0, x²+2x-1/3=0, x²+2x+1=1+1/3, (x+1)²=4/3, x=±2√3/3-1
(3). (x-1)²-2(x-1)+1=1/2, (x-1-1)²=1/2, (x-2)=±√2/2, x=2±√2/2.
7.
x²-2x/3+1=0, x²-2x/3+(1/3)²=1/9-1, (x-1/3)²=-8/9
8.
3x²-6x-1=0, x²-2x+1-1-1/3=0, (x-1)²=4/3, x-1=±2√3/3, x=1±2√3/3
2x²-5x-4=0, x²-5x/2=2, x²-5x/2+(5/4)²=2+25/16, (x-5/4)²=57/16, x=5/4±√57/4=(5±√57)/4.
(1). x²+x+0.5²=1+0.25, (x+0.5)²=1.25=5/4, x=±√5/2-1/2=(±√5-1)/2.
(2). 3x²+6x-1=0, x²+2x-1/3=0, x²+2x+1=1+1/3, (x+1)²=4/3, x=±2√3/3-1
(3). (x-1)²-2(x-1)+1=1/2, (x-1-1)²=1/2, (x-2)=±√2/2, x=2±√2/2.
7.
x²-2x/3+1=0, x²-2x/3+(1/3)²=1/9-1, (x-1/3)²=-8/9
8.
3x²-6x-1=0, x²-2x+1-1-1/3=0, (x-1)²=4/3, x-1=±2√3/3, x=1±2√3/3
2x²-5x-4=0, x²-5x/2=2, x²-5x/2+(5/4)²=2+25/16, (x-5/4)²=57/16, x=5/4±√57/4=(5±√57)/4.
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