[latex]2.101 a) \ x^2-10x+25=0\ (x-5)^2=0\ x-5=0\ x=5\ \ b)\ 4x^2=12x-9\ 4x^2-12x+9=0\ (2x-3)^2=0\ 2x-3=0\ x=frac{3}{2}\ \ [/latex] [latex]c)\ 9x^2+1=6x\ 9x^2-6x+1=0\ (3x-1)^2=0\ 3x-1=0\ x=frac{1}{3}\ \ d)\ 16x^2+25=40x\ 16x^2-40x+25=0\ (4x-5)^2=0\ 4x-5=0\ x=frac{5}{4}\ \ [/latex] [latex]e) 9x^2=12x-4\ 9x^2-12x+4=0\ (3x-2)^2=0\ 3x-2=0\ x=frac{2}{3}\ \ f)\ 25x^2+10x+1=0 \ (5x+1)^2=0\ 5x+1=0\ x=-frac{1}{5} [/latex] [latex]2.102 a)\ x^2+4x-5=0\ (x-1)(x+5)=0\ x-1=0 vee x+5=0\ x=1 vee x=-5\ \ b)\ -x^2+4x+21=0\ (7-x)(x+3)=0\ 7-x=0 vee x+3=0\ x=7 vee x=-3\ \ [/latex] [latex]c) \ 2x^2+5x-12=0\ Delta=5^2-4*2*(-12)=25+96=121\ x_{1}=frac{-5-11}{4}=frac{-16}{4}=-4\ x_{2}=frac{-5+11}{4}=frac{6}{4}=frac{3}{2}\ \ d) \ 3x^2+7x-20=0\ Delta=7^2-4*3*(-20)=289\ x_{1}=frac{-7-17}{6}=frac{-24}{6}=-2\ x_{2}=frac{-7+17}{6}=frac{10}{6}=frac{5}{3}[/latex]
