نویسنده : امیر انصاری

1. $$
   x^2-12x+9=0
   $$
   
2. $$
   5x^2-20x-1=0
   $$
   
3. $$
   -2x^2+x-1=0
   $$
   
4. $$
   0.5x^2+2.1x+3.6=0
   $$
   
5. $$
   -1.2x^2-5.1x-7.4=0
   $$
   
6. $$
   \frac{1}{2}x^2+3x-6=0
   $$
   

پاسخ

1. $$
   x^2-12x+9=0\\
   (x^2-12x+36)-36+9=0\\
   (x-6)^2-27=0
   $$
   
2. $$
   5x^2-20x-1=0\\
   5(x^2-4x)-1=0\\
   5(x^2-4x+4-4)-1=0\\
   5(x-2)^2-20-1=0\\
   5(x-2)^2-21=0
   $$
   
3. $$
   -2x^2+x-1=0\\
   -2 \bigl( x^2-\frac{1}{2}x \bigr)-1=0\\
   -2 \bigl( x^2 - \frac{1}{2}x+\frac{1}{16}-\frac{1}{16} \bigr)-1=0\\
   -2 \bigl( x-\frac{1}{4} \bigr)^2 + \frac{1}{8}-1=0\\
   -2 \bigl( x-\frac{1}{4} \bigr)^2 - \frac{7}{8}=0
   $$
   
4. $$
   0.5x^2+2.1x+3.6=0\\
   0.5(x^2+4.2x)+3.6=0\\
   0.5(x^2+4.2x+4.41-4.41)+3.6=0\\
   0.5(x+2.1)^2-2.205+3.6=0\\
   0.5(x+2.1)^2+1.395=0
   $$
   
5. $$
   -1.2x^2-5.1x-7.4=0\\
   -1.2(x^2+4.25x)-7.4=0\\
   -1.2(x^2+4.25x+4.515625-4.515625)-7.4=0\\
   -1.2(x+2.125)^2+5.41875-7.4=0\\
   -1.2(x+2.125)^2-1.98125=0
   $$
   
6. $$
   \frac{1}{2}x^2+3x-6=0\\
   \frac{1}{2}(x^2+6x)-6=0\\
   \frac{1}{2}(x^2+6x+9-9)-6=0\\
   \frac{1}{2}(x+3)^2-\frac{9}{2}-6=0\\
   \frac{1}{2}(x+3)^2-\frac{21}{2}=0
   $$